```3.2
October 02, 2014
Get out your notes from yesterday.
We will do the back side today.
Bell Ringer
Solve using substitution
3x+ 2y = 1
&shy;2x + y = 4
1. Solve one equation for a variable
2. Substitute the equation from 1. back into the other equation.
3. Solve
3.2 Solving Systems Algebraically
Substitution: • Good to use when one equation is already solved for a variable
• Useful if at least one variable has a coefficient of +1 or &shy;1.
Elimination
• Works well with any equation
• Goal is to start by rewriting the equations so one variable has opposite coefficients.
Solve using elimination
1. Pick a variable to eliminate.
8x + 2y = 4
&shy;2x + 3y = 13
2. Multiple one or both equations by a real number so that selected variable has opposite coefficients
3. Add equations and solve for remaining variable.
4. Substitute solution from step 3 back into any of the equations to find the remaining variable.
4. Substitute solution back into equation from step 1.
Solve 12x &shy; 3y = &shy;9
&shy;4x + y = 3
Solve 6x + 15y = &shy;12
&shy;2x &shy; 5y = 9
3.2
October 02, 2014
HW
3.2 Worksheet G
# 1&shy;9, 11&shy;19, 21&shy;29
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