Luttrell 2012
93
Name: ______________________
Date: _____
6i – Systems of Equations - Elimination
Solving a s
y
stem with Substitution either means you are good with fractions or you use it mostly
when a variable has a coefficient of one. Most times elimination will prove easier.
E
x
ample: Solve the s
y
stem: 5
x
+ 3
y
= 18
3
x
- 2
y
= 7
Step I: choose variable
y
ou want to eliminate. We choose to eliminate
y
for this example.
Step II: Multipl
y
each row b
y
a number so that the coefficients for
y
are opposites. The first
equation was multiplied by 2 and the second by 3. The equations are still balanced!
10
x
+ 6
y
= 36
9
x
- 6
y
= 21
Step III: Add the equations together. One variable must disappear or else we made a mistake!
By adding equal items to both sides, the result is a balanced equation.
19
x
+ 0 = 57
Step IV: Solve for remaining variable.
19
x
= 57
x
= 3
Step V: Repeat process with other variable or do a substitution.
3(3) - 2
y
= 7
9 - 2
y
= 7
-2
y
= -2
y
= 1
Solve. Sketch a graph to confirm results.
1.
x
+
y
= 5
2. 4
x
+ 3
y
= 7
3.
y
= -2
x
+ 1
x
-
y
= 1
3
x
- 2
y
= 1
y
= -3
x
+ 3
4. 5
x
-
y
= 6
5. 5
x
- 3
y
= 12
6. 4
x
+ 5
y
= 2
3
x
- 2
y
= -2 3
x
+ 2
y
= 11 3
x
+ 2
y
= 5
