Welcome to my web page on linear equations. Just like cheerleading, math can take you to a place of flips, tumbles, and round-offs. Get ready for a major cheerathon! GO MATHLETES!
Substitution Method
1. Solve one of the equations for one of its variables.
2. Substitute the expression from step 1 into the other equation and solve for the other variable.
3. Substitute the value from step 2 into the revised equation from step 1 and solve
.
6x+y=-2 4x-3y=17
6x+y=-2 revise to y=-6x-2
4x-3(-6x-2)=17 x=1/2
y=-6(1/2)-2 y=-5
The solution is (1/2, -5)
2x-y=6 2x+2y=-9
2x-y=6 revise to y=2x-6
2x+2(2x-6)=-9 x=1/2
y=2(1/2)-6 y=-5
The solution is (1/2, -5)
Elimination Method
1. Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables.
2. Add the revised equation from step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable.
3. Substitute the value obtained in step 2 into either of the original equations and solve for the other variable.
6x+3y=3 8x+4y=4
-4(6x+3y=3) -3(8x+4y=4)
-24x-12y=-12+24x+12y=12
0=0
There are an infinite number of solutions.
-11x+6y=1 3x+2y=-3
3(3x+2y=-3
-11x+6y=1+9x+6y=-9
x=-1/2
9(-1/2)+6y=-9 y=-7.5
The solution is (-1/2, -7.5)