Solve the system of equations by the elimination method

7x-4y=-3

3x-9y=-45

x=3

y=6

Step-by-step explanation:

The goal of the elimination method is to cancel out one of the variables when the equations are added or subtracted. Let's say we will cancel out the two "x" first. Multiply both of the equations entirely so that the "x" is the same.

{7x - 4y = - 3} * 3 = > 21x - 12y = - 9

{3x - 9y = - 45} * 7 = > 21x - 63y = - 315

Subtract the first equation from the second equation. Subtract each term separately and remember subtracting a negative number becomes adding.

. 21x - 12y = - 9

- 21x - 63y = - 315

. 0x + 51y = 306 Notice x variable cancels out

. 51y = 306 < = Divide both sides by 51

. y = 6

Substitute y=6 into any of the equations. Then isolate x. I will use 7x-4y=-3.

7x - 4y = - 3

7x - 4 (6) = - 3 <=simplify

7x - 24 = - 3 Start isolating x by bringing everything to the right side

7x = - 3 + 24 <=add 24 to both sides. This cancels out 24 on the left.

7x = 21 <=divide both sides by 7

x = 3

The solution of the system is (3, 6).