Solve Linear Equations
Solving Systems of Linear Equations: Graphing
All or No Solutions
Solve Linear Systems of Equations
Make Systems of Linear Equations
100
2( 1 - 2x) = x - 3
x = 1
100
How many possible solutions can a system of linear equations have?
one, none/zero, or infinitely many solutions (the line itself)
100
Solve the system:
2x+y=9
-2x-y=-9
All solutions
100
y = 3x + 5
y = -2x + 20
(3, 14)
100
Two people are racing. They start at the same time. One runs at 3 m/s, the other runs 4 m/s. What is a systems of equations that describes this?
d=3t
d=4t
200
9 - 2b + 6 = -3b - 15 + 4b
b = 10
200
How many solutions will a set of parallel lines have?
Zero
200
Solve the system:
y=2x+4
y=2x+5
No solution
200
y = -3x + 10
y = -2x + 6
(4,-2)
200
Two plants are growing. One started at a height of 4 cm and is growing 6 cm a week. The other started at a height of 7 and is growing 3 cm a week.
What system of equations describes this scenario.
h=4+6w
h=7+3w
300
p - 5(p + 4) = p - (8 - p)
p = -2
300
What is the solution to these system of equations?
(2, 2)
300
Solve the system:
y+3x=7
y=-3x+7
All solutions
300
y = 3/2 x + 7
x = -4
(-4, 1)
300
There are a total of 140 tickets to be sold for the school play. Adult tickets sell for $15 and student tickets sell for $10. The total ticket revenue is $1630.
Create a system of equations that describes this system.
A+S=140
15A+10S=1630
400
3(c - 1) + 2(3c + 1) = -(3c + 1)
c = 0
400
Prove the solution given on the graph by setting the equations equal to each other:
(2,2)
400
Solve the system:
9x+3y=7
9x+3y=5
No solution
400
y = 3x + 2
2x + y =47
(9, 29)
400
What system describes the following,
A man is hiking up a mountain. He is ascending at 5 km/h. A helicopter takes off 100 km below him and is ascending at 40 km/h.
h=5t+100
h=5t
500
-5/6(8 + 5b) = 75 + 5/3b
b = -14
500
What is the solution to the system of linear equations?
infinitely many solutions
500
Solve the system:
y-2x=4
y-4=2x
All solutions
500
y = -2x + 5
2x + 3y = 31
(-4, 13)
500
What system describes the following,
The SPCA has 100 cats to be adopted. They adopt out 4 per day. A pet store has 50 cats to be adopted. They adopt out 2 per day.
C=100-4d
C=50-2d