Solve by Graphing
Solve by Elimination
Solve by Substitution
Word Problems
Steps/Number of Solutions
100
How many solutions does this graph have?
No Solution
100
x + 5y = 12
-x + y = 0
(2,2)
100
x + y = 2
y = 3
(-1,3)
100
Set up the system of equations (DO NOT SOLVE!!!)
Ms. Jackson bought a bag of candy and 2 bottled drinks, and spent $18. Ms. Phillips bought 2 bags of candy and a bottled drink, and spend $22. How much does a bag of candy cost? How much does a bottled drink cost?
x + y = 18
2x + y = 22
100
A system of equations has the same y-intercept and the same slopes. How many solutions does the system have?
Infinite solutions
200
What is the solution to the system of equations shown in the graph?
(1, -3)
200
-4x - 2y = -12
4x + 8y = -24
(6,-6)
200
y=−x+4
2x+y=1
(1,3)
200
Set up the system of equations (DO NOT SOLVE!!!)
A school sold tickets to a basketball game. Adult tickets cost $8 and student tickets cost $5. In total, 50 tickets were sold and $310 was collected. How many of each type of ticket was sold?
x + y = 50
8x + 5y = 310
200
What could be a first step in solving the system of equations by elimination?
5x - 4y = 30
-5x - 9y = 15
a. Multiply the top equation by 4 to eliminate y's
b. Multiply the bottom equation by 2 to eliminate the constants
c. Add the equations to eliminate the x's
d. Add the equations to eliminate the y's
C
300
What is the solution to the system of equations shown in the graph?
(3, -1)
300
5x + y = 9
10x - 7y = -18
What is (1,4)?
300
y = 6x - 11
-2x - 3y = -7
(2,1)
300
Set up the system of equations (DO NOT SOLVE!!!)
The perimeter of a rectangle is 72 cm.
The length is twice the width.
Find the dimensions of the rectangle.
2x + 2y =72
x = 2y
300
What is the first step in solving this equation by substitution?
y = 2x + 1
3x - 4y = 15
a. Distribute the 4
b. Substitute 2x + 1 into the second equation for y
c. Combine like terms
d. Graph
B
400
Find the slope and y intercept of the line, and say how many solutions the system would have.
Line 1: y = 2x + 3
Line 2: y = 2x + 5
Line 1: m = 2, b = 3
Line 2: m = 2, b = 5
No solution
400
-4x + 9y = 9
x - 3y = - 6
(9,5)
400
-3x + 3y = 4
-x + y = 3
no solution
400
Harold had a summer lemonade stand where he sold small cups for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?
x + y = 155
1.25x + 2.50y = 265
400
How many solutions does the following system have?
2x + y = 10
3x - 3y = 9
One solution
500
How many solutions does the system graphed have?
Infinitely many solutions
500
2x + 8y = 6
-5x - 20y = -15
infinite solutions
500
2y - x = 4
10y - x = 20
(0,2)
500
Notebooks and planners were sold at a school fundraiser. On Monday, 40 total items were sold.
The school sold notebooks for $3 each and planners for $7 each and raised a total of $196.
How many notebooks and planners were sold?
21 Notebooks, 19 Planners
500
Two equations are graphed and the lines never intersect.
One line has a slope of 3 and a y-intercept of –2.
The other line has a slope of 3 and a y-intercept of 5.
Write the system of equations. What is the solution?
y = 3x - 2
y = 3x + 5
NO SOLUTION