Solve by Substitution
Solve the systems of equations using substitution:
y=3x-10
x=2
(2,-4)
Solve the systems of equations using Elimination:
-x - 5y = 4
x + 7y = -8
(6, -2)
How many solutions would a system of linear equations have if the equations have the same slope and different y-intercepts?
No Solutions
Two lines are graphed on the same coordinate plane. The lines only intersect at the point (1,2). Which system could represent the equations of the two lines?
A. y = x - 1 and y = -3x + 7
B. y=3x - 1 and y=10x - 8
C. y = 2x + 1 and y = x + 2
B.
y=3x - 1
y=10x - 8
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)
Solve the systems of equations using Elimination:
2x - 3y = 10
2x - y = 2
(-1, -4)
How many solutions would a system of linear equations have if the equations have the same slope and have the same y-intercept?
Infinite Solutions
Two lines are graphed on the same coordinate plane. The lines only intersect at the point (0,5). Which system could represent the equations of the two lines? Select ALL that apply.
A. x=0 and y=5
B. 2x + 5y = 10 and y= 2x - 5
C. y=x+5 and x=3y-15
A. x=0 and y=5
AND
C. y=x+5 and x=3y-15
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
Solve the systems of equations using Elimination:
-3x - 5y = 2
6x + 10y = 0
No Solution
Is there 1 solution, No solution, or Infinite solutions for the following question?
3x - y = 19
y = 3x + 10
No Solutions
You and a friend are invited to a party. You both bring pizza and chips. Your friend brought 3 pizzas and 4 bags of chips and spent $48.05. You brought 5 pizzas and 2 bags of chips and spent $67.25.
What is the cost of each pizza and each bag of chips?
A pizza costs $12.35
A bag of chips costs $2.75
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
Solve the systems of equations using Elimination:
x + 8y = 22
3x + 4y = -14
(-10, 4)
How many solutions does the system have?
3y + 4x = 6
12y + 16x = 24
Infinite Solutions
Blake and Jake went shopping. Blake bought three shirts and one pair of pants and spent $38. Jake bought four shirts and three pairs of pants and spent $71.50.
What was the cost of each shirt and each pair of pants?
Shirt costs $8.50
Pants costs $12.50
Solve the systems of equations using substitution:
y = 8x -7
16x - 2y = 14
Infinitely Many Solutions
Solve the systems of equations using Elimination:
-10x + 3y = -30
-4x + 2y = -10
(3.75, 2.5)
How many solutions does the system have?
-6y + 2 = -4x
y - 2 = x
Different slopes
One solution
y=2/3x+1/3
y=x+2
Sylvie and Leah went shopping. Sylvie spent $120 on 3 pairs of jeans and 6 blouses. Leah spent $90 on 2 pairs of jeans and 5 blouses.
The scenario can be represented by the following system of equations where x is the cost of jeans and y is the cost of a blouse.
3x + 6y = 120
2x + 5y = 90
Solve the system to determine the cost of each item.
Now, find the total cost if someone else buys 4 pairs of jeans and 2 blouses.
Jeans (x) costs $20 and a blouse (y) costs $10.
If someone buys 4 pairs of jeans and 2 blouses they will spend $100.
4(20) + 2(20) = 100