Download Example 1 Solving by Addition Solve 3x+2y = 19 (1) 5x

1.5 Solving Linear Systems by Elimination
The substitution method for solving a system of equations
works well when at least one variable in one or both
equations has a coefficient of 1 or -1. With other coefficients,
substitution may lead to complicated equations with fractions.
Is there another algebraic method that we can use?
Yes! We can use the method
of ELIMINATION.
Example 1
Solve
Solving by Addition
3x+2y = 19 (1)
5x-2y = 5 (2)
1
Step 1: Add equation (1) to equation (2).
3x+2y = 19
5x-2y
=5
______
8x = 24
x=3
Adding the equations eliminates the y-terms
and allows us to solve for x.
Step 2:
Substitute 3 for x in equation (1).
3(3)+2y = 19
9+2y = 19
2y = 10
y=5
2
Step 3: Check in equation (2).
LS = 5x-2y
= 5(3)-2(5)
= 15 - 10
=5
RS = 5
∴ the solution is (3,5)
Example 2
Solve
Solving by Subtraction
2x-3y = 12 (1)
5x-3y = 21 (2)
3
Example 3
Solve Using Multiplication
and Subtraction
Solve
3x+2y = 2 (1)
4x+5y = 12 (2)
Example 4
Solve Using Multiplication
and Subtraction
Solve
0.3x-0.5y = 1.2 (1)
0.7x-0.2y = -0.1 (2)
4
Example 5
Solve Using Multiplication
and Addition
Solve
4a - _
b=9
(1)
3 4
_
_
5a + b = 1
6
(2)
5