Question 1

Solve the problem using the elimination method.
-There were 490 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1070. How many adults and how many children attended?

Accepted Answer

The system of equations is: $3a + c = 1070$ and $a + c = 490$. Subtracting the second equation from the first gives $2a = 580$, so $a = 290$. Substituting $a = 290$ into $a + c = 490$ gives $c = 200$.

Question 2

Solve the system of equations by the elimination method.
-x + 5y = 2 -4x + 6y = -8

Accepted Answer

To solve the system of equations by the elimination method, we can multiply the first equation by 4 to make the coefficients of x in both equations equal in magnitude but opposite in sign. This gives us:4(x + 5y) = 4(2) => 4x + 20y = 8-4x + 6y = -8Adding these two equations together eliminates x:(4x - 4x) + (20y + 6y) = 8 - 826y = 0y = 0Substituting y = 0 into the first equation:x + 5(0) = 2x = 2Therefore, the solution is (2, 0).

Question 3

Solve the system of equations by the elimination method.
--0.8x + 0.4y = 4.8 0.1x - 0.1y = -0.7

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 multiply the first equation by 1 and the second equation by 4 to get:-0.8x + 0.4y = 4.80.4x - 0.4y = -2.8Adding these equations together to eliminate y gives:-0.4x = 2x = -5Substituting x = -5 into one of the original equations to solve for y:-0.8(-5) + 0.4y = 4.84 + 0.4y = 4.80.4y = 0.8y = 2Therefore, the solution to the system of equations is x = -5 and y = 2, which corresponds to choice C.

Question 4

Solve the problem using the elimination method.
-A salesman sold $200 more than the rest of the sales staff. If the sales total for the day was $2050, how much did the rest of the sales staff sell?

Accepted Answer

Let x be the amount sold by the rest of the sales staff. The salesman sold x + $200. Together, they sold $2050. So, the equation is x + (x + $200) = $2050. Solving this, 2x + $200 = $2050, then 2x = $1850, and x = $925.

Question 5

Solve the problem using the elimination method.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $5.00. Another customer buys 4 hot dogs and 3 bags of potato chips for $9.00. Find the cost of each item.

Accepted Answer

The answer of Solve the problem using the elimination method.
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Question 6

Solve the system of equations by the elimination method.
--7x - 6y = -36 -3x + 4y = 24

Accepted Answer

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

Question 7

Solve the system of equations by the elimination method.
-9x + 9y = -45 -4x - 6y = 20

Accepted Answer

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

Question 8

Solve the system of equations by the elimination method.
-3x - 5y = 2 18x - 30y = 12

Accepted Answer

The second equation is a multiple of the first (multiplied by 6). This means the two equations are essentially the same line, hence there are infinitely many solutions.

Question 9

Solve the system of equations by the elimination method.
-2.5x + 0.3y = 10.6 0.5x + 0.9y = 3.8

Accepted Answer

To eliminate one variable, multiply the second equation by 5 to align the coefficients of x: 2.5x + 0.3y = 10.6 and 2.5x + 4.5y = 19. Subtract the first from the second to eliminate x, solve for y, then substitute back to find x. The solution is (4, 2).

Question 10

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

The two angles are supplementary, so their sum is 180°. Let x be the smaller angle, then the other angle is 3x + 40. The equation is x + 3x + 40 = 180. Solving for x gives x = 35°, which is the smaller angle.

Question 11

Solve the system of equations by the elimination method.
-x - 3y = -5 4x - 4y = 12

Accepted Answer

Multiply the first equation by 4 and the second equation by 1 to get:4x - 12y = -204x - 4y = 12Subtract the second equation from the first equation to get:-8y = -32Divide both sides of the equation by -8 to get:y = 4Substitute y = 4 into the first equation to get:x - 3(4) = -5x - 12 = -5Add 12 to both sides of the equation to get:x = 7Therefore, the solution to the system of equations is (x, y) = (7, 4).

Question 12

Solve the system of equations by the elimination method.
-x + 3y = 15 -6x + 4y = 20

Accepted Answer

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

Question 13

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 sum of angles in a triangle is 180°, and since it's a right triangle, the two acute angles must sum to 90°. Let x be one acute angle, then the other is 2x + 54°. The equation is x + 2x + 54 = 90. Solving for x gives x = 12°, making the other angle 78°.

Question 14

Solve the system of equations by the elimination method.
-5x - 6y = -5 15x - 18y = 15

Accepted Answer

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

Question 15

Solve the problem using the elimination method.
-There were 38,000 people at a ball game in Los Angeles. The day's receipts were $229,000. How many people paid $11 for reserved seats and how many paid $4 for general admission?

Accepted Answer

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

Question 16

Solve the system of equations by the elimination method.
-

Accepted Answer

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

Question 17

Solve the system of equations by the elimination method.
-

Accepted Answer

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

Question 18

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

The two angles are supplementary, meaning they add up to 180°. Let x be the smaller angle, then the larger angle is 6x + 5°. The equation is x + (6x + 5) = 180. Solving for x gives x = 25°, making the larger angle 6(25) + 5 = 155°.

Question 19

Solve using the elimination method.
-x + 6y = 26 2x + 6y = 22

Accepted Answer

The answer of Solve using the elimination method.
-x + 6y...

Question 20

Solve the system of equations by the elimination method.
-0.3x + 0.5y = 3.1 x - 0.1y = 1.5

Accepted Answer

To solve the system of equations by the elimination method, we first align the equations and then manipulate them to eliminate one variable. The given equations are:1) $0.3x + 0.5y = 3.1$2) $x - 0.1y = 1.5$To eliminate $y$, we can multiply the second equation by 5 to make the coefficients of $y$ in both equations equal in magnitude but opposite in sign:$5(x - 0.1y) = 5(1.5)$$5x - 0.5y = 7.5$Now, we have the system:1) $0.3x + 0.5y = 3.1$2) $5x - 0.5y = 7.5$Adding these two equations to eliminate $y$, we get:$0.3x + 5x = 3.1 + 7.5$$5.3x = 10.6$$x = 2$Substitute $x = 2$ into one of the original equations to solve for $y$. Using the second equation:$2 - 0.1y = 1.5$$0.1y = 2 - 1.5$$0.1y = 0.5$$y = 5$Therefore, the solution is $x = 2$, $y = 5$, which corresponds to choice D) (2, 5).

Quiz 9: Systems of Equations

Solve the problem using the elimination method. -There were 490 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1070. How many adults and how many children attended?

Solve the system of equations by the elimination method. -x + 5y = 2 -4x + 6y = -8

Solve the system of equations by the elimination method. --0.8x + 0.4y = 4.8 0.1x - 0.1y = -0.7

Solve the problem using the elimination method. -A salesman sold $200 more than the rest of the sales staff. If the sales total for the day was $2050, how much did the rest of the sales staff sell?

Solve the problem using the elimination method. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $5.00. Another customer buys 4 hot dogs and 3 bags of potato chips for $9.00. Find the cost of each item.

Solve the system of equations by the elimination method. --7x - 6y = -36 -3x + 4y = 24

Solve the system of equations by the elimination method. -9x + 9y = -45 -4x - 6y = 20

Solve the system of equations by the elimination method. -3x - 5y = 2 18x - 30y = 12

Solve the system of equations by the elimination method. -2.5x + 0.3y = 10.6 0.5x + 0.9y = 3.8

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. -x - 3y = -5 4x - 4y = 12

Solve the system of equations by the elimination method. -x + 3y = 15 -6x + 4y = 20

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 system of equations by the elimination method. -5x - 6y = -5 15x - 18y = 15

Solve the problem using the elimination method. -There were 38,000 people at a ball game in Los Angeles. The day's receipts were $229,000. How many people paid $11 for reserved seats and how many paid $4 for general admission?

Solve the system of equations by the elimination method. -

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 using the elimination method. -x + 6y = 26 2x + 6y = 22

Solve the system of equations by the elimination method. -0.3x + 0.5y = 3.1 x - 0.1y = 1.5