Mr. Sims
Solve by using the addition method.
1. 4 5y + 4z = 9
-5 4y + 5z = 9
multiply the top by 4 and
the bottom by –5 to cancel the y
Algebra 1
Section 7.3 B
Solving Linear Systems
by Addition Method
20y + 16z = 36
-20y – 25z = - 45
-9z = -9
z=1
5y + 4z = 9
substitute into any
equation with y and z
5y + 4(1) = 9
5y + 4 = 9
-4 -4
5y = 5
y=1
Mr. Sims
2.
10a + 16b = 140
-2 5a – 8b = 60
multiply bottom by -2
10a + 16b = 140
-10a + 16b = -120
32b = 20
20
b
32
5
b
8
10a + 16b = 140
2
substitute into any
equation with a and b
5
10a  16   140
8
10a + 10 = 140
-10
-10
10a = 130
a = 13
Mr. Sims
3.
x + 3y = 12
-3y + x = 30
arrange bottom equation so
that like terms are in columns
x + 3y = 12
x – 3y = 30
2x = 42
x = 21
x + 3y = 12
21 + 3y = 12
-21
substitute into any
equation with x and y
-21
3y = -9
y = -3
Mr. Sims
4. y = x – 9
x + 8y = 0
arrange top equation so
that like terms are in columns
-x + y = -9
x + 8y = 0
9y = -9
y = -1
x + 8y = 0
x + 8(-1) = 0
x–8=0
substitute into any
equation with x and y
+8 +8
x=8
Mr. Sims
5.
3y = -5x + 15
-y = -3x + 9
arrange both equations
5x + 3y = 15
3 3x – y = 9
multiply bottom by 3
5x + 3y = 15
9x – 3y = 27
14x = 42
x=3
3y = -5x + 15
3y = -5(3) + 15
3y = -15 + 15
3y = 0
y=0
substitute
Mr. Sims
Solve the system of equations using the addition method.
1.) x – 4y = 14
-x + 3y = -11
2.) 3x + y = 6
-3x + 4y = 9
3.) x + 3y = -3
x – 4y = 11
4.) 5x + 2y = 5
3x + y = 2
5.) 4x – 5y = -18
5x + 4y = -2
6.) 4x = -3 + y
y = -6x – 7
7.) 5y – 3x = -4
3x + 4y = 13
8.) 3y = 5x + 15
6x = 2y - 18
Algebra 1
Section 7.3 B
Assignment
Mr. Sims
Any rebroadcast, reproduction, or other use of the pictures and
materials from this site and presentations, without the express
written consent of Mr. Sims, is prohibited.
© Mr. Sims. All rights reserved.
Mr. Sims