The schematics of Algebra

The Substitution Method

The Linear Combination Method

Step 1. Solve one of the equations for one of it's variables.

Step 2. Substitute the expression from Step 1 into the other equation and solve for the other variable.

Step 3. Substitute the value from Step 2 into the revised equation from Step 1 and solve.

Step 1. Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables.

Step 2. Add the revised equations from Step 1. Combining Like terms will eliminate one of the variables. Solve for the remaining variable.

Step 3. Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.

Example:

3x+4y= -4

x+2y=2

1.Solve equation 2 for x

x+2y=2

x=-2y +2 (Rewrite the Equation)

2.Substitute the value of expression for x into Equation 1 and solve for y.

3x+4y = -4

3(-2y+2)+4y= -4

y=5

3.Substitute the value of y into revised Equation 2 and solve for x.

x= -2y+2

x= -2(5)+2

x= -8

Example:

2x-4y=13

4x-5y=8

1. Multiply the first equation by -2 so that the x-coefficients differ only in sign.

-2(2x-4y=13) ---> -4x+8y=-26

2. Add the revised equations and solve for y.

(-4x+8y=-26)+(4x-5y=8)=(3y=-18)

y=-6

3. Substitute the value of y into one of the original equations. Solve for x.

2x-4y=13

2x-4(-6)=13

2x+24=13

x=-11/2