THE 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.

3x+4y=-4

x+2y=2

1. Solve Equation 2 for x. x+2y=2. x=-2y+2
2. Substittutethe expression for xinto 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
4. The solutionis (-8,5). *click on me.*

THE LINEAR COMBINATION 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 equations fron Step 1. Combinig like terms will elimate one of the variables. Slove for the remaining variable.
3. Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.

2x-4y=13

4x-5y=8

1. Multiply the first equation by -2 so that the x-coefficients differonly in sign. -2(2x-4y=13) -4x+8y=-26
2. Add the revised equations and solve for y. y=-6
3. Substitute the value of y into one of the original equations. Solve for x. x=-11/2
4. The solution is (-11/2,-6).

THE GRAPHING METHOD

1. System of two linear equations-in two variables x and y consists of two equations of the following form. Ax+By=C Equation 1. Dx+Ey=F Equation 2.
2. Solution-of a system of linear equations in two variables is ordered pair (x,y) that satisfies each equation.

2x-3y=1

x+y=3

WORD PROBLEM

A caterer is planning a party for 64 people. The customer has $150 to spend. A$39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make?

Equation1 People per pan of pasta = 14 (people)

Pans of pasta = p (pans)

Sandwich trays = s

People at the party = 64 (people)

Equation2 Price per pan of pasta = 39 (dollars)

Pans of pasta = P

Price per sandwich tray = 12 (dollars)

Sandwich trays = S

Money to spend on food = 150 (dollars)

14p + 6s = 64

39p + 12s = 150

Multilply equation 1 by -2 so that the coefficients of S differ only in sign. -28p - 12s = -128

Add the revised equations and solve for P. p = 2

Substitute the value of pinto one of the original equations and solve for S. s = 6

The caterer should make 2 pans of pasta and 6 sandwich trays for the party.