Systems with Graphs
What is the solution?
y=-5x-4
y=2x+3
(-1,1)
Solve the systems of equations:
-3x + 4y = -2
y = -5
(-6, -5)
Solve the systems of equations:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
Olivia had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each type did she sell?
Define the variables and write the system of equations.
x= # of large lemonade cups sold
y= # of small lemonade cups sold
1.25y+ 2.25x= 265
y + x= 155
Solve the system by graphing:
y = -1/2x + 3
y = 5
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
Solve the systems of equations:
-3x - 5y = 2
3x + 5y = 7
No Solution
Ms Carew bought 2 new shirts and a dress for $45. She then went back and bought another shirt and 4 dresses for $75. What was the cost of each shirt?
Define the variables and write the system of equations.
s= price of each shirt
d= price of each dress
2s + d= 45
s + 4d= 75
Solve by graphing:
y = -2/3x + 3
y = 2x – 5
(3,1)
Solve the systems of equations:
y = -2x - 9
3x -6y = 9
(-3, -3)
Solve the systems of equations:
-6x - 10y = 4
6x + 10y = 0
No Solution
Define the variables and write the system of equations.
Zeke sells blueberries and grapes. Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zeke made $55 from selling a total of 33 pounds of blueberries and grapes. How many pounds of blueberries and grapes did Zeke sell?
b= # of lbs. of blueberries sold
g= # of lbs. of grapes sold
2.50b + 1.25g= 55
b + g= 33
Solve by graphing:
y = -1/2x + 4
x + 2y = 8
Infinite Solutions
Solve the systems of equations:
-8x - 5y = -24
-x + y = 10
(-2, 8)
Solve the systems of equations:
-x + 2y = -13
2x + 3y = 12
(9,-2)
Maci put 200 inches of ribbon along the border of a rectangular bulletin board. If the length of the bulletin board is 2 less than 4 times the width, then what are the dimensions?
Define the variables and write the system of equations.
l=length
w=width
l= 4w - 2
2w + 2l= 200
Solve the systems of linear equations by graphing:
y = -x + 7
5x + 5y = 10
No solutions
Solve the systems of equations:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions
Solve the systems of equations:
-15x + 6y = -36
4x - 3y = 11
(2, -1)
Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle.
Define the variables and write the system of equations.
b= larger angle
a= smaller angle
a + b= 180
b= 10a +15