# Solving Systems of Linear Equations

### Multiplication Method

Step 1: Solve for the First Variable

write out the equation 3x+2y=1 and 4x+3y=2

then you multiply the variables by 3 to get 9x+6y=3 and 8x+6y=4.

After that you cancel out the 6y on each side, and minus the 9x and 8x.

so the first variable would be x=7

Step 2: solve for the second variable

you plug in for the x on with either equation

so the equation can be 3(7)+2y=1 so it would be 21+2y=1.

so you minus 21 on each side so you can isolate the y and the equation would end up being 2y=-20, then you divide by 2 on each side to get the y by it self so y=-10

Step 3: Write your solution

The solution would be (7,-10) because x=7 and y=-10

x always goes first

Step 4: Check your solution

3(7)+2(-10)=1 it would end up being 21+-20=1, then you add 20 on each side so it would be 21=21

But you have to check each equation

4(7)+3(-10)=2 it would end up being 28+30=2, then you minus 30 on each side so it would be 28=28