Question

Find the solution to the system of equations.

y=3x-4
y=-2x+6

Answer 1

Explanation:

There a few ways to solve this system. Since each equation is set equal to y on the left side, that means that we can set the right side of each equation to be equal to each other. So,

3x - 4 = -2x + 6

This can now be solved for x:

5x - 4 = 6 (added 2x to each side)

5x = 10 (added 4 to each side)

x = 2 (divided each side by 5)

Now that we know what x must be, we can plug 5 in for x in either of the equations and solve for y:

y = 3(5) - 4

y = 6 -4

y=2

This means y should be 2. To make sure this answer is correct, we can plug our y and x numbers into the OTHER equation to see if it makes sense:

(2) = -2(2) + 6

2 = -4 + 6

2=2

That looks right, so x = 2 and y = 2