Question

Solve the system of equations below using the substitution method. x = y + 7 / 2 4x − 2y = 8

Answer 1

Answer:

y = -3

x = $\frac{1}{2}$

Step-by-step explanation:

4(y + $\frac{7}{2}$) - 2y = 8  Distribute the 4.  Multiply everything in the parentheses by 4

4y + 14 - 2y = 8           4$(\frac{7}{2})$ = $\frac{28}{2}$ = 14  Combine the like terms 4y and -2y

2y + 14 = 8         Subtract 14 from both sides

2y =  -6               Divide both sides by 2

y = -3  

Plug -3 in for y in either original equation.

4x - 2y = 8

4x -2(-3) = 8

4x + 6 = 8    Subtract 6 from both sides

4x = 2  Divide both sides by 4

x = $\frac{2}{4}$ = $\frac{1}{2}$

Check:

x = y + $\frac{7}{2}$

$\frac{1}{2}$ = -3+ $\frac{7}{2}$

$\frac{1}{2}$ = $\frac{-6}{2}$ + $\frac{7}{2}$

$\frac{1}{2}$ = $\frac{1}{2}$

4x - 2y = 8

4($\frac{1}{2}$) - 2(-3) = 8

2 + 6 = 8

8 = 8