Question

How to solve y=-2x+8 and y-2=x

Answer 1

(x, y) = (2, 4)

Explanation:

You want to solve the system of equations ...

• y = -2x +8
• y -2 = x

Solution

There are numerous ways to solve this system of equations. One of the simplest is to use a graphing calculator. (See the attachment)

(x, y) = (2, 4)

Substitution

The second equation gives an expression for x that can be substituted into the first equation:

y = -2(y -2) +8

3y = 12 . . . . . . . . add 2y and simplify

y = 4

4-2 = x = 2

The solution is (x, y) = (2, 4).

Elimination

The y-variable has a coefficient of 1 on the left side of the equal sign, so we can eliminate the y-variable by subtracting the second equation from the first.

(y) -(y -2) = (-2x+8) -(x)

2 = -3x +8 . . . . . . . . . . . simplify

3x = 6 . . . . . . . . . . add 3x-2

x = 2 . . . . . . . . divide by 3

y = -2(2) +8 = 4 . . . . . substitute for x in the first equation

The solution is (x, y) = (2, 4).