Question

Examine the system of equations. y = negative one-half x + 1 y = 2x + 6 Use substitution to solve for x and

Answer 1

x=-2 y=2

Explanation:

it is -2,2 as the other thing

Answer 2

x = - 2 , y = 2

( - 2, 2)

Explanation:

`y = - (1)/(2) x + 1 \\ y = 2x + 6`

first equation add 1/2 to both sides

second equation subtract 2x from both sides

`y + (1)/(2) x = 1 \\ y - 2x = 6`

Solve the first equation

`y + (1)/(2) x = 1`

subtract x/2 from both sides

`y = - (1)/(2) x + 1`

substitute
`- (x)/(2) + 1` for y in the other equation

`- (1)/(2) x + 1 - 2x = 6`

add

`(1)/(2) x` to 2x

`- (5)/(2) x + 1 = 6`

subtract 1 from both sides

`- (5)/(2) x = 5`

divide both sides by
`- (5)/(2)`

x = - 2

substitute the value of x into an equation

`y = - (1)/(2) ( - 2) + 1`

distribute

y = 1 + 1

y = 2

x = -2, y = 2

( - 2, 2)