Find the solution to the system of equations by substitution.
- x - y = -4
A) (0, 6)
B) (-1, 6)
C) (1, 5)
D) no solution

Question

Find the solution to the system of equations by substitution.
- x - y = -4
A) (0, 6) 
B) (-1, 6) 
C) (1, 5) 
D) no solution

Quizplus · Accepted Answer

Solve the first equation for x:
x = y - 4
Substitute this expression for x in the second equation and solve for y:
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 (y - 4) - y = -4
10y - 44 = -4
10y = 40
y = 4
Substitute y = 4 back into the first equation to solve for x:
x = 4 - 4
x = 1
Therefore, the solution is (1, 4), which corresponds to choice C. We can solve for one of the variables in terms of the other in one of the equations and substitute that expression into the other equation. 
From the first equation, we can isolate x by adding y to both sides: 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 x = y - 4 
Then we can substitute y - 4 for x in the second equation: 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 (y - 4) - y = -8 
Expanding and simplifying: 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00y - 4*11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 - y = -8 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00y - y = -8 + 4 
10y = -4 
y = -2/5 
Then we can substitute y = -2/5 into the first equation to solve for x: 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 x - (-2/5) = -4 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 x = -4 + 2/5 
11ebb63d_1b3a_f1e8_b851_d10a2f97acf6_TB8475_00 x = -18/5 
The solution is therefore (x, y) = (-18/5, -2/5), which corresponds to choice C.

Find the Solution to the System of Equations by Substitution