Solving Systems of Linear Equations
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