Systems with Graphs
Solving by Substitution
Solving by Elimination
Linear Inequalities
Word Problems
100
What is the solution?
(-1,1)
100
Solve the systems of equations:
-3x + 4y = -2
y = -5
(-6, -5)
100
Solve the systems of equations:
10x + y = 20
-4x - y = -50
(-5, 70)
100
which way would you shade in this inequality?
y> 2x+5
Above the line!
100
A bookstore sells hardcover novels for $20 each and paperback novels for $15 each.
The manager wants to make at least $450 in total sales today.
What inequality represents the possible numbers of hardcover and paperback books sold?
20x+15y≥450
200
Solve using Graphing
y= 2x + 1
y= -x + 7
(2, 5)
200
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
200
Solve the systems of equations:
-3x - 5y = 2
3x + 5y = 7
No Solution
200
When should you have dotted line?
When the inequality is < or >
200
A concert venue charges x dollars for adult tickets and y dollars for child tickets.
Three adult tickets and five child tickets cost $85.
Four adult tickets and two child tickets cost $68.
Write and solve a system of equations to find the price of one adult ticket and one child ticket.
Adult: $12.14
Child: $9.72
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
Solve the systems of equations:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
Solve the systems of equations:
-6x - 10y = 4
6x + 10y = 0
No Solution
300
2x-3y<=-2
y>=-4x+24
is (5,4) a solution to the system? Why?
Yes, (5,4) is a solution to the system because the point is on the solid line of both inequalities.
300
Jared is buying fruit cups, x, and juice boxes, y, for a school picnic. The system of inequalities models how many of each item Jared needs to buy and how much he can spend. Which of the following points represents a viable solution to the system?
x + y ≥ 160
3x + 5y ≤ 680
A. (100, 80)
B. (120, 60)
C. (80, 100)
D. (140, 40)
B. (120,60)
400
How many solutions are there?
Infinitely Many Solutions
400
Solve the systems of equations:
-8x - 5y = -24
y = x + 10
(-2, 8)
400
Solve the systems of equations:
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
400
y<=1/2x+5
y<1/2x+5
Is (-10,0) in the solution set of the above system? Why?
No, because (-10,0) is on the dotted line of the second inequality.
400
Liam wants to sell handmade candles at a market for $15 each.
The materials for each candle cost $5.50, and the booth rental at the market costs $45 for the day.
How many candles must Liam sell for his revenue to equal his expenses?
At least 5 candles
500
Solve the systems of linear equations by graphing:
500
Solve the systems of equations:
y = 8x - 7
16x - 2y = 14
Infinitely Many Solutions
500
Solve the systems of equations:
-5x + y = -3
4x - y = 11
(-8, -43)
500
Graph the system of inequalities.
y >2
y < 2x - 4
Is (0,0) a solution to the system? Why?
No!
500
Samantha starts walking at a rate of 4 miles per hour on a road toward a park that is 12 miles away.
Alex leaves the park at the same time and walks toward Samantha along the same road at 3 miles per hour.
How many hours will pass before they meet?
Around 1.71 hours