13
Graph the lines.
3x -
y=
3x - y = 13
2x + 2y = -10
2x
+
2y
=
-1
0
(2, -7)?
Graph the lines.
Substitution method:
3x - y = 13
1. Solve first equation for one of
the variables.
y = 3x - 13
3x -
y=
13
2x + 2y = -10
2x
+
2y
=
-1
0
2. Substitute (3x - 13) for y in the
second equation.
2x + 2(3x - 13) = -10
3. Solve the equation from step 2.
2x + 6x - 26 = -10
8x = 16
x=2
4. Substitute the result from step 3
back into either of the 2 original equations
and solve for the remaining variable.
3x - y = 13
3(2) - y = 13
6 - y = 13
-y = 7
y = -7
5. Write the x and y
values as an ordered
pair.
(2, -7)
Solve the system. (Find the intersection point).
3x - y = 13
2x + 2y = -10
Substitution method
3x - y = 13
y = 3x - 13
x + y = -5
x + 3x - 13 = -5
4x = 8
x=2
x + y = -5
2 + y = -5
y = -7
(2, -7)
Graph the lines.
(-1, -1)?
Substitution method
y = 3x + 2
-3x + y = 2
8x - 15(3x + 2) = 7
-3(-1) + y = 2
8x - 45x - 30 = 7
3+y=2
-37x = 37
y = -1
x = -1
(-1, -1)
Graph the lines.
(7, 3)?
Solve the system.
Substitution method
x - 4y = -2
x - 4y = -2
x = 4y - 2
x - 4(7/4) = -2
-3(4y - 2) + 8y = -1
x - 7 = -2
-12y + 6 + 8y = -1
x=5
-4y = -7
(5, 7/4)
y = 7/4
-9x + 6y = 30
-7x = 49
x = -7
-3(-7) + 2y = 10
2y = -11
y = -11/2
18x - 10y = -14
-18x + 12y = 6
2y = -8
y = -4
-6x + 4(-4) = 2
-6x = 18
x = -3
3x + 2y = 6
-6x - 3y = -6
x = 5y + 11
2(5y + 11) + 7y = -3
y = 3x + 8
4x - 2(3x + 8) = -1
3
3x = 5y + 11
x = (5/3)y + 11/3
2[(5/3)y + 11/3] + 7y = -3
-6x + 10y = -22
6x + 21y = -9
31y = -31
y = -1
** a false statement like 0 = 7 means no solution
x = # of oranges
y = # of grapefruits
.50x + .75y = 13.25
.75x + 1.25y = 21