Question

Solve the system.
y= -2x + 1

y= 2x - 3

Answer 1

x=1 and y=−1

Explanation:

Step: Substitute −2x + 1 for y in y=2x−3:

y = 2x − 3

−2x + 1 = 2x − 3

−2x + 1+ − 2x = 2x − 3 + −2x (Add -2x to both sides)

−4x + 1 = −3

−4x + 1 + −1 = −3 + −1 (Add -1 to both sides)

−4x = −4

`(-4x)/(-4) =(-4)/(-4)` (Divide both sides by -4)

x = 1

Step: Substitute 1 for x in y = −2x + 1:

y = −2x + 1

y = (−2)(1)+1

y = −1 (Simplify both sides of the equation)

Answer 2

Equation 1: y = -2x + 1

Equation 2: y = 2x - 3

Since both equations already have y isolated, we are able to simply set the right side of both equations equal to each other. Since we know that the value of y must be the same, we can do this.

-2x + 1 = 2x - 3

1 = 4x - 3

4 = 4x

x = 1

Then, we need to plug our value of x back into either of the original two equations and solve for y. I will be plugging x back into equation 2 above.

y = 2x - 3

y = 2(1) - 3

y = 2 - 3

y = -1

Hope this helps!! :)