Chapter 3 Lesson 2 Solving Systems of Equations Algebraically

Vocabulary Substitution Method- One equation is solved for one variable in terms of the other, then that expression is substituted for the variable in the other equation Elimination Method- Eliminate one of the variables by adding or subtracting the equations

Solutions Same as last section No Solutions When eliminating one variable, you eliminate the other and get an unequal equation, such as 0 = 2. One Solution Using substitution or elimination to get a single ordered pair as a solution. Infinitely Many Solutions When eliminating one variable, you eliminate the other and get an equal equation, such as 0 = 0.

Substituting Pick one of the equations, does not matter which one Solve for a variable, usually the one that’s easiest to solve for Substitute what that variable equals in the other equation for that variable 2x+y=8 3y+4x=4 Top equation 2x+y=8 y=8-2x Substitute it into bottom equation 3(8-2x)+4x=4 2(10)+y=8 24-6x+4x=4 20+y=8 24-2x=4 y=-12 -2x=-20 x=10 Solution: (10,-12)

Example 2r + s = 11 6r – 2s = -2

Example 5a – b = 17 3a + 2b = 5

Example 3s + 2t = -3 s + 1 / 3 t = -4

Other Examples

Elimination Subtracting one equation from the other to eliminate a variable 2x+3y=7 2(3)+3y=7 5x+3y=16 6+3y=7 3y=1 2x+3y=7 y= 1 / 3 -5x-3y=-16 __________ -3x=-9 x=3 Solution: (3, 1 / 3 )

Example m – n = 9 7m + n = 7

Example r + 4s = -8 3r + 2s = 6

Example 6d + 3f = 12 2d= 8 - f

Other Examples

Homework Worksheet 3-2