Question

What is the solution of the system of equations? -y+3x=6 y=-6x+12

Answer 1

(2,0)

Explanation:

I'm going to use substitution since one of the variables in one of the equation is already solved for.

-y+3x=6

y=-6x+12

I'm going to replace the first y with the second y which is (-6x+12).

This gives me:

-(-6x+12)+3x=6

Distribute:

6x-12+3x=6

Combine like terms:

9x-12=6

Add 12 on both sides:

9x=18

Divide both sides by 9:

x=2

If x=2 and y=-6x+12, then y=-6(2)+12=-12+12=0.

The solution (the intersection) is (2,0).

Answer 2

x = 2

y = 0

Explanation:

We can solve using substitution, substitute y in the first equation with the second equation:

-(-6x + 12) + 3x = 6

Distribute the negative sign:

6x - 12 + 3x = 6

Combine like terms:

9x - 12 = 6

Isolate the variable and solve for x by adding 12 in both sides:

9x = 18

x = 2

Substitute 2 with x in any equation to find the value of y:

-y + 3(2) = 6

-y + 6 = 6

Subtract 6 in both sides to isolate the variable:

-y = 0

0/-1 = 0

y = 0

Our answer would be x = 2 and y = 0