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5.3
Solving a System of Linear Equations by Elimination Notes
HW 29: P. 251 #3-19 odds, and 37-41 odds
Solving a System of Linear Equations by Elimination
Step 1 Write each equation in ax + by =
c form, or order like terms consistently.
Step 2 Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has
opposite coefficients.
Step 3 Add the equations to eliminate one of the variables.
Step 4 Solve the resulting equation.
Step 5 Substitute the value from Step 4 into one of the original equations and solve for the other variable.
In Exercises 1–6, solve the system of linear equations by elimination. Check your solution.
1.
2x + 3y =
10
2.
− 2 x − y =− 2
3.
2x + y =
12
− x − 3y =
3
4.
3 x − 18 =
y
5.
3x − 2 y =
−2
4x − 3y =
−4
144 Algebra 1
Student Journal
4x + 3y =
6
x + 2y =
20
2x + y =
19
6.
− 3 x − 5 y =− 7
− 4x − 3y =
−2
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All rights reserved.
In Exercises 1–6, solve the system of linear equations by elimination. Check your solution.
1.
x − 3y =
2
2.
− 2x + 3y =
1
− x + 2 y =− 3
3.
x + y =
7
4.
5x + 2 y =
8
5.
3x + 4 y =
−1
2x − 5 y =
−7
7x − 6 y =
9
5x + 2 y =
19
6.
− 2x − 5 y =
10
− 5 x + 12 y =
8
2x − 8 y =
0
In Exercises 14–16, solve the system of linear equations using elimination or substitution.
7.
2x − 5 y =
1
2 x= 9 − 3 y
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All rights reserved.
8.
4 x − 6 =−2 y
x +9 =
y
Algebra 1
Student Journal
145