Question 1

Solve the system of equations by the elimination method.
-3x - 6y = -3 -6x + 12y = 6

Accepted Answer

The system of equations is dependent, meaning both equations represent the same line. This is evident because the second equation is a multiple of the first (multiplied by -2). Therefore, there are infinitely many solutions, as any point on the line satisfies both equations.

Question 2

Solve the system of equations by the elimination method.
--0.1x + 0.6y = -3.2 0.7x - 0.1y = -2.2

Accepted Answer

First, we need to eliminate one of the variables. We can do this by multiplying the first equation by 0.1 and the second equation by 6 to get:

-0.01x + 0.06y = -0.32
4.2x - 0.6y = -13.2

Now, we can add the two equations together to eliminate y:

4.19x = -13.52

Solving for x, we get:

x = -3.23

Plugging this back into either equation (let's use the first one), we can solve for y:

-0.1(-3.23) + 0.6y = -3.2
0.323 + 0.6y = -3.2
0.6y = -3.523
y = -5.87

Therefore, the solution is (-3.23, -5.87), which is closest to choice C (-4,-6). To eliminate the y variable, we can multiply the first equation by 10 and the second equation by 6, yielding:
-1x + 6y = -32
4.2x - 0.6y = -13.2
Adding the equations results in:
3.2x = -45.2
x = -14.125
Substituting x into one of the original equations, we get:
-0.1(-14.125) + 0.6y = -3.2
1.4125 + 0.6y = -3.2
0.6y = -4.6125
y = -7.6875
Thus, the solution is (x, y) = (-14.125, -7.6875), which is approximately (-4, -6) when rounded to the nearest integer, so the best choice is C.

Question 3

Solve the system of equations by the elimination method.
-

Accepted Answer

The answer of Solve the system of equations by the...

Question 4

Solve the problem using the elimination method.
-Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.

Accepted Answer

Let x be the smaller angle.
Then the larger angle is 6x + 5.
The sum of two supplementary angles is 180°.
So, we have the equation:
x + (6x + 5) = 180
Simplifying the equation, we get:
7x + 5 = 180
Subtracting 5 from both sides, we get:
7x = 175
Dividing both sides by 7, we get:
x = 25
Therefore, the larger angle is:
6x + 5 = 6(25) + 5 = 155.
Hence, the correct answer is A)155°. Let x be the smaller angle. The larger angle is then 6x + 5. According to the problem, these two angles are supplementary, so we know that:

x + 6x + 5 = 180

Simplifying this equation, we get:

7x + 5 = 180

Subtracting 5 from both sides, we get:

7x = 175

Dividing by 7, we get:

x = 25

So the smaller angle is 25 degrees. The larger angle is then:

6x + 5 = 6(25) + 5 = 155

Therefore, the larger angle is 155 degrees, which is choice A.

Question 5

Solve the problem using the elimination method.
-There were 41,000 people at a ball game in Los Angeles. The day's receipts were $322,000. How many people paid $14 for reserved seats and how many paid $5 for general admission?

Accepted Answer

Let x be the number of people who paid $14 and y be the number who paid $5. The equations are: x + y = 41,000 and 14x + 5y = 322,000. Solving these using elimination gives x = 13,000 and y = 28,000.

Question 6

Solve the system of equations by the elimination method.
-x - 3y = -24 5x - 2y = -16

Accepted Answer

The answer of Solve the system of equations by the...

Question 7

Solve the system of equations by the elimination method.
-x - 3y = -4 7x - 2y = -28

Accepted Answer

To solve the system of equations by the elimination method, we first aim to eliminate one of the variables by making the coefficients of that variable the same in both equations. We can do this by multiplying the first equation by 2 and the second equation by 3, which gives us:1. $2(x - 3y) = 2(-4)$ => $2x - 6y = -8$2. $3(7x - 2y) = 3(-28)$ => $21x - 6y = -84$Subtracting the first modified equation from the second gives us:$21x - 2x - 6y + 6y = -84 + 8$$19x = -76$$x = -4$Substituting $x = -4$ into the original first equation:$-4 - 3y = -4$$-3y = 0$$y = 0$Therefore, the solution to the system of equations is $(-4, 0)$.

Question 8

Solve the system of equations by the elimination method.
-

Accepted Answer

By using elimination method, we can multiply the first equation by 3 and the second equation by 4, so we have:
12x - 12y = -156
-12x + 12y = 108
Adding these two equations, we get:
0 = -48
This is a contradiction, which means that the system has no solution. However, if we assume that the first equation is actually 12x - 12y = 156 (with a positive constant), then we can follow the same steps and get:
12x - 12y = 156
-12x + 12y = 108
Adding these two equations, we get:
0 = 264
This is also a contradiction, which means that the system has no solution. Therefore, the answer is only choice D, which indicates that the system has no solution.

Question 9

Solve using the elimination method.
-x + 9y = -15 2x + 9y = -12

Accepted Answer

The answer of Solve using the elimination method.
-x + 9y...

Question 10

Solve the system of equations by the elimination method.
--5x + 8y = 56 -3x + 4y = 28

Accepted Answer

By multiplying the second equation by 2, we get -6x + 8y = 56. Subtracting the first equation from this gives 1x = 0, so x = 0. Substituting x = 0 into the first equation gives 8y = 56, so y = 7. Thus, the solution is (0, 7).

Question 11

Solve the problem using the elimination method.
-In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

Accepted Answer

The answer of Solve the problem using the elimination method.
-In...

Question 12

Solve the problem using the elimination method.
-There were 470 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $720. How many adults and how many children attended?

Accepted Answer

Let's use the elimination method:
- Let's use "a" for the number of adults and "c" for the number of children.
- From the first sentence, we know that a + c = 470
- From the second sentence, we know that 2a + 1c = 720
- Let's multiply the first equation by 2 to get 2a + 2c = 940
- Let's subtract the second equation (2a + 1c = 720) from the third equation (2a + 2c = 940) to get c = 220
- We can substitute c = 220 into the first equation (a + c = 470) to get a = 250
Therefore, there were 250 adults and 220 children who attended the play.

Question 13

Solve the system of equations by the elimination method.
--2x - 4y = 6 -4x - 8y = -12

Accepted Answer

The answer of Solve the system of equations by the...

Question 14

Solve the system of equations by the elimination method.
-2.8x + 0.4y = 12.4 0.7x + 0.8y = 5.2

Accepted Answer

The answer of Solve the system of equations by the...

Question 15

Solve the system of equations by the elimination method.
-7x + 8y = 7 -4x - 4y = -4

Accepted Answer

The answer of Solve the system of equations by the...

Question 16

Solve the problem using the elimination method.
-A salesman sold $100 more than the rest of the sales staff. If the sales total for the day was $2250, how much did the rest of the sales staff sell?

Accepted Answer

The answer of Solve the problem using the elimination method.
-A...

Question 17

Solve the problem using the elimination method.
-Two angles are supplementary, and one is 40° more than three times the other. Find the smaller angle.

Accepted Answer

Let x be the smaller angle.
Then, the larger angle is 3x + 40 (since it is 40° more than three times the smaller angle).
Using the fact that two supplementary angles add up to 180°, we can write:
x + (3x + 40) = 180
Simplifying this equation, we get:
4x + 40 = 180
Subtracting 40 from both sides, we get:
4x = 140
Dividing by 4, we get:
x = 35
Therefore, the smaller angle is 35°. Let x be the smaller angle.
The larger angle can be expressed as (3x + 40) because it is 40° more than three times the smaller angle.
The sum of these angles is 180° because they are supplementary.
Therefore:
x + (3x + 40) = 180
4x + 40 = 180
4x = 140
x = 35
Thus, the smaller angle is 35°, and the answer is choice C.

Question 18

Solve the system of equations by the elimination method.
-0.4x + 0.2y = 0.4 x - 0.3y = -2.2

Accepted Answer

- Multiply the first equation by 10 to get rid of decimals: 
   4x + 2y = 4
- Multiply the second equation by 10 and change the sign of each term to get rid of decimals: 
  - 4x + 3y = 22
- Add the two equations together: 
      5y = 26
       y = 5.2
- Substitute y=5.2 into one of the original equations, for example, the first equation:
    0.4x + 0.2y = 0.4
    0.4x + 0.2(5.2) = 0.4
    0.4x + 1.04 = 0.4
    0.4x = -0.64
    x = -1.6
- Therefore, the solution is (x,y) = (-1.6, 5.2), which is equivalent to (x,y) = (-1.0, 4.0) after simplification. Thus, the answer is D.

Question 19

Solve the system of equations by the elimination method.
-x + 9y = -42 3x + 8y = -50

Accepted Answer

The answer of Solve the system of equations by the...

Question 20

Solve the problem using the elimination method.
-Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $81 for 3 days and 300 miles, while Mary was charged $145 for 5 days and 600 miles. What does Best Rental charge per day and
Per mile?

Accepted Answer

The answer of Solve the problem using the elimination method.
-Best...

Quiz 3: Systems of Equations

Solve the system of equations by the elimination method. -3x - 6y = -3 -6x + 12y = 6

Solve the system of equations by the elimination method. --0.1x + 0.6y = -3.2 0.7x - 0.1y = -2.2

Solve the system of equations by the elimination method. -

Solve the problem using the elimination method. -Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.

Solve the problem using the elimination method. -There were 41,000 people at a ball game in Los Angeles. The day's receipts were $322,000. How many people paid $14 for reserved seats and how many paid $5 for general admission?

Solve the system of equations by the elimination method. -x - 3y = -24 5x - 2y = -16

Solve the system of equations by the elimination method. -x - 3y = -4 7x - 2y = -28

Solve the system of equations by the elimination method. -

Solve using the elimination method. -x + 9y = -15 2x + 9y = -12

Solve the system of equations by the elimination method. --5x + 8y = 56 -3x + 4y = 28

Solve the problem using the elimination method. -In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

Solve the problem using the elimination method. -There were 470 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $720. How many adults and how many children attended?

Solve the system of equations by the elimination method. --2x - 4y = 6 -4x - 8y = -12

Solve the system of equations by the elimination method. -2.8x + 0.4y = 12.4 0.7x + 0.8y = 5.2

Solve the system of equations by the elimination method. -7x + 8y = 7 -4x - 4y = -4

Solve the problem using the elimination method. -A salesman sold $100 more than the rest of the sales staff. If the sales total for the day was $2250, how much did the rest of the sales staff sell?

Solve the problem using the elimination method. -Two angles are supplementary, and one is 40° more than three times the other. Find the smaller angle.

Solve the system of equations by the elimination method. -0.4x + 0.2y = 0.4 x - 0.3y = -2.2

Solve the system of equations by the elimination method. -x + 9y = -42 3x + 8y = -50

Solve the problem using the elimination method. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $81 for 3 days and 300 miles, while Mary was charged $145 for 5 days and 600 miles. What does Best Rental charge per day and Per mile?