Graphical Solution of Systems of Linear Equations

1. Graphical Solution of
Systems of Linear Equations

2. 2x-3y=1
2x-3(0)=1
2x=1
x=1/2
Ex. 1: Solve the system: 2x-3y=1 and
5x+2y=12
2x-3y=1
2(0)-3y=1
-3y=1
y=-1/3
5x+2y=12
5x+2(0)=12
5x=12
x=12/5
x=2 2/5
5x+2y=12
5(0)+2y=12
2y=12
y=12/2
y=6
x 0 1/2
y -1/3 0
x 0 2 2/5
y 6 0

3. We then plot the points (0,-⅓) and (½, 0) and (0,6) and (2 ⅖, 0) in the
coordinate plane.
x 0 1/2
y -1/3 0
x 0 2 2/5
y 6 0
Based on the point of intersection of the
lines, the solution set of the system is (2,1).
To check, we compute the set of ordered
pairs from both the equations.
2x-3y=1
2(2)-3(1)=1
4-3=1
1=1
5x+2y=12
5(2)+2(1)=12
10+2=12
12=12

4. 2x+y=6
2x+0=6
2x=6
x=6/2
x=3
Ex. 2: Solve the system 2x+y=6 and 4x+y=8
2x+y=6
2(0)+y=6
y=6
4x+y=8
4x+0=8
4x=8
x=8/4
x=2
4x+y=8
4(0)+y=8
y=8
x 0 3
y 6 0
x 0 2
y 8 0

5. We then plot the points (0,6) and (3, 0) and (0,8) and (2, 0) in the
coordinate plane.
x 0 3
y 6 0
x 0 2
y 8 0
Based on the point of intersection of the
lines, the solution set of the system is (1,4).
To check, we compute the set of ordered
pairs from both the equations.
2x+y=6
2(1)+4=6
2+4=6
6=6
4x+y=8
4(1)+4=8
4+4=8
8=8