Question

Use the substitution method to solve the system of equations.

5x + 2y = 1
y = -x + 2
A. (-2, 4)
B. (-1, 3)
C. (-3, 5)
D. (-3, 8)

Answer 1

By using the substitution method, the system of equations 5x + 2y = 1 and y = -x + 2 is solved to find x = -1 and y = 3, corresponding to option B.

Step-by-step explanation:

To solve the system of equations using the substitution method, first substitute the expression for y from the second equation into the first. The two equations given are:

• 5x + 2y = 1
• y = -x + 2

Substitute y in the first equation:

1. 5x + 2(-x + 2) = 1
2. 5x - 2x + 4 = 1
3. 3x + 4 = 1
4. 3x = 1 - 4
5. 3x = -3
6. x = -1

Substitute x back into y = -x + 2 to find y:

1. y = -(-1) + 2
2. y = 1 + 2
3. y = 3

The solution to the system of equations is x = -1 and y = 3, which corresponds to option B.