Systems of Equations

Solutions to Systems

100

Describe the solution to a system when looking at a graph

Where the two lines intersect each other

200

Is (-4,-7) a solution to the system:

y=x-3

y=5x+1

No, because when you substitute -4 in for x and -7 in for y in the second equation, you do not end with a true statement.

300

Is (-4,-2) a solution to the system:

x+2y=-8

y=-x+2

Yes, when you substitute -4 in for x and -2 in for y, you end with a true statement for BOTH equations

400

Is (-2,-4) a solution to the system:

7x+2y=6

y=-4

No, when you substitute -2 in for x and -4 in for y, you do not end with a true statement for the first equation.

500

Is (4,3) a solution to the system:

x-y=1

-x=4y-16

Yes, when you substitute 4 in for x and 3 in for y, you end with a true statement for BOTH equations

Graphing Method

100

What is the first point you plot when graphing a linear equation?

The y-intercept

200

Describe how you would use the following slope to graph a line.

2/3

Up 2 and Right 3 from the y-intercept.

OR

Down 2 and Left 3 from the y-intercept.

300

Describe how you would use the following slope to graph a line.

-3

Down 3 and Right 1 from the y-intercept.

OR

Up 3 and Left 1 from the y-intercept.

400

If two lines are graphed and they overlap, what is the solution to the system?

Infinite Solutions

500

If two lines are graphed and they do not cross, what is the solution to the system?

No Solution

Substitution Method

100

Solve the system using Substitution

y=-8x-21

y=3

(-3,3)

200

Solve the system using substitution

-x+2y=-8

y=2x-10

(4,-2)

300

Solve the system using substitution

y=x+3

5x-4y=-20

(-8,-5)

400

Solve the system using substitution

3x+3y=12

y=-3x+8

(2,2)

500

Solve the system using substitution

y=5x-13

y=4x-10

(3,2)

Elimination Method

100

Solve the system using elimination

-x+3y=-6

x+8y=6

(6,0)

200

Solve the system using elimination

-3x-10y=23

-3x-5y=-2

(9,-5)

300

Solve the system using elimination

-2x+20y=18

10x-10y=0

(1,1)

400

Solve the system using elimination

14x-y=7

7x-4y=-21

(1,7)

500

Solve the system using elimination (hint: you may have to multiply BOTH equations)

-3x-6y=-18

4x+5y=6

(-6,6)

Spiraled Review

100

Evaluate the expression

f(-2) if f(x)=|2x+3|

f(-2)=1

200

Solve the equation

-6-5(1+3n) = -86

n=5

300

Solve the equation

92 = -4-4(8x-8)

x = -2

400

(2x⁴)³

8x¹²

500

³Simplify the exponential expression. Your answer should contain only positive exponents.

4v³ x 2v^-4 x 3v⁴

24v³