Solve by Graphing
Solve by Substitution
Solve by Elimination
Check
100
Solve the system of equations graphically.
y = 2x + 3
y = -5x - 4
(-1,1)
100
Solve the systems of equations using substitution:
y = 9x - 9
y = 9
9 = 9x - 9 Substitute x into an equation
18 = 9x y = 9
2 = x Solution: (2 , 9)
100
Solve the systems of equations using Elimination:
14x + 2y = 26
-14x - 6y = -50
14x + 2y = 26 Substitute y into an equation
-14x - 6y = -50 14x + 2(6) = 26
-4y = -24 14x + 12 = 26
y = 6 14x = 14
x = 1
Solution: (1 , 6)
200
Solve the system of equations graphically.
y = (5/3)x + 2
y = -3
200
Solve the systems of equations using substitution:
y = -8
y = -2x - 12
-8 = -2x - 12 Substitute x into an equation
4 = -2x y = -8
-2 = x Solution: (-2 , -8)
200
Solve the systems of equations using Elimination:
-3x - 5y = 2
3x + 5y = 7
-3x - 5y = 2
3x + 5y = 7
0 = 9
Never true! No solution!
300
Solve the system of equations graphically.
300
Solve the systems of equations using substitution:
y = 2x - 15
y = 5x
5x = 2x - 15 Substitute x into an equation
3x = -15 y = 5(-5)
x = -5 y = -25
Solution: (-5 , -25)
300
Solve the systems of equations using Elimination:
-6x - 10y = 4
6x + 10y = -4
-6x - 10y = 4
6x + 10y = -4
0 = 0
Always true! Infinite Solutions!
400
Solve the system of equations graphically.
y = (1/2)x - 3
3y = (3/2)x - 9
Infinitely Many Solutions
400
Solve the systems of equations using substitution:
y = 3x
-3x - y = -24
-3x - 3x = -24 Substitute x into an equation
-6x = -24 y = 3(4)
x = 4 y = 12
Solution: (4 , 12)
400
Solve the systems of equations using Elimination:
-3x - 24y = -66
9x + 12y = -42
-9x - 72y = -198 Substitute y into an equation
9x + 12y = -42 9x + 12(4) = -42
-60y = -240 9x + 48 = -42
y = 4 9x = -90
x = -10
Solution: (-10 , 4)
400
Check to see if the solution (3,2) is correct for the system of equations below.
-2x + 6y = 6
-7x + 8y = -5
-2x + 6y = 6 -7x + 8y = -5
-2(3) + 6(2) = 6 -7(3) + 8(2) = -5
-6 + 12 = 6 -21 + 16 = -5
6 = 6 -5 = -5
500
Solve the system of equations graphically.
2y = 4x + 4
9y = 18x + 9
No Solutions
500
Solve the systems of equations using substitution:
x = -2y + 5
x + y = 2
-2y + 5 + y = 2 Substitute y into an equation
-y + 5 = 2 x + 3 = 2
-y = -3 x = -1
y = 3 Solution: (-1 , 3)
500
Solve the systems of equations using Elimination:
2y + x = 3
-y - 2x = 21
2y + x = 3 Substitute x into an equation
-2y - 4x = 42 2y + (-15) = 3
-3x = 45 2y = 18
x = -15 y = 9
Solution: (-15 , 9)
500
Check to see if the solution (-4,3) is correct for the system of equations below.
-3x - 3y = 3
y = -5x - 17
-3x - 3y = 3 y = -5x - 17
-3(-4) - 3(3) = 3 3 = -5(-4) - 17
12 - 9 = 3 3 = 20 - 17
3 = 3 3 = 3