Answer:
x = - 2 , y = 2
( - 2, 2)
Step-by-step explanation:
[tex]y = - \frac{1}{2} x + 1 \\ y = 2x + 6[/tex]
first equation add 1/2 to both sides
second equation subtract 2x from both sides
[tex]y + \frac{1}{2} x = 1 \\ y - 2x = 6[/tex]
Solve the first equation
[tex]y + \frac{1}{2} x = 1[/tex]
subtract x/2 from both sides
[tex]y = - \frac{1}{2} x + 1[/tex]
substitute [tex]- \frac{x}{2} + 1[/tex] for y in the other equation
[tex]- \frac{1}{2} x + 1 - 2x = 6[/tex]
add
[tex]\frac{1}{2} x[/tex] to 2x
[tex]- \frac{5}{2} x + 1 = 6[/tex]
subtract 1 from both sides
[tex]- \frac{5}{2} x = 5[/tex]
divide both sides by [tex]- \frac{5}{2}[/tex]
x = - 2
substitute the value of x into an equation
[tex]y = - \frac{1}{2} ( - 2) + 1[/tex]
distribute
y = 1 + 1
y = 2
x = -2, y = 2
( - 2, 2)
