Solving by Graphing
Solve by graphing:
y = 3/2x + 1
y = -1/2x + 5
(2, 4)
The solution to the system of equations:
8x - y = -25
-8x + 6y = -10
(-4, -7)
The solution to the system
y = 3x - 1
7x + 2y = 37
(3, 8)
Write a system of equations for the following situation:
The school is selling tickets to the musical. On the first day, the school sold 13 student tickets and 1 adult ticket for a total of $125. The school took in $198 on the second day by selling 6 student tickets and 2 adult tickets.
13x+y=125
6x+2y=198
How many solutions does the system have?
y=-3/2x+5
y=3/2x-5
One solution
Solve by graphing:
y = 3x - 2
y = -x - 2
(0, -2)
The solution to the system of equations:
3x - 7y = 16
-9x + 2y = -29
(3, -1)
The solution to the system:
x = 4y
2x + 3y = 22
(8, 2)
Kayky and Miguel are planting bushes and trees. Kayky spend $66 on 5 bushes and 4 trees. Miguel spent $75 on 5 bushes and 5 trees. Find the cost of one bush and one tree.
$6 for one bush and $9 for one tree
How many solutions does this system have?
4x-3=y
4x-y=-3
No solutions
Solve by graphing:
y=1/4x+3
2x-y=4
(4, 4)
The solution to the system:
2x + 3y = 6
3x + 5y = 15
(-15, 12)
The solution to the system
y = x - 2
3x - y = 16
(7, 5)
A shopper bought 6 shirts and 8 hats for $70. A week later, at the same prices, he bought 3 shirts and 2 hats for $22. What was the cost of one shirt?
$3
Consider the system:
7x + 2y = 24
8x + 2y = 30
The solution to the original system is the pair x=6 and y=-9. Explain why it makes sense that this pair of values is also a solution to the equation 15x+4y=54.
15x+4y=54 is the sum of 7x + 2y = 24 and 8x + 2y = 30. When we add 8x + 2y to one side of the equation and 30 to the other, we are adding equal amounts, so the equation is still true. The solution to the original equation will still be a solution to the new equation.
Solve by graphing:
8x + 14y = 28
−6x − 7y = −28
(7, -2)
The solution to the system
−7x + y = −19
−2x + 3y = −19
(2, -5)
The solution to the system
3s - 2t = 4
t-2s = - 1
(-2, -5)
What is the number of each type of ticket sold in the following situation: Tickets to a football game cost $5.00 if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
400 advanced tickets and 200 game-day tickets
How many solutions does the system have?
4x-6y=10
-6x+9y=-15
Infinite
Solve by graphing:
y=2x-1
x+1/3y=3
(2, 3)
The solution to the system:
−14 = −20y − 7x
10y + 4 = 2x
(2, 0)
The solution to the system:
y = 2x - 8
y = 5x - 23
(5, 2)
A nature center charges $35.25 for a yearly membership and $6.25 for a single admission. Last week it sold a combined total of 50 yearly memberships and single admissions for $660.50. Write and solve a system of equations to find how many memberships and how many single admissions were sold.
35.25x+6.25y=660.50
x+y=50
12 memberships and 38 single admissions
The following system of equations has exactly one x,y pair for its solution.
5x-3y=1
x-2y=3
If we triple each side of the second equation, explain why the same x,y pair that is a solution to the system is also a solution to this new equation.
A solution to the system will be a solution for both of the original equations.
By multiplying by the same quantity on both sides, we will have created an equivalent equation. This equation will have the same solutions as the original second equation.