Question

Determine a method other than graphing that could be used to solve this system of linear equations. Explain how to solve the system of equations using this method.

{y=-x+6
{y=3x+2

Answer 1

set x equal to 1 then solve


`y = - 1 + 6`

`y = 5`
then


`y = 3 * 1 + 2`

`y = 5`

Answer 2

y = -1 + 6 = 5

Explanation:

Because they are both solved for y, set the equations equal to each and solve for x:

-x + 6 = 3x + 2

6 - 2 = 3x + x

4 = 4x

1 = x

Substitute the x-value, 1, into one of the original equations to find the y-value:

y = -1 + 6 = 5

The solution is the point (1, 5).