PRACTICE
Graph the following systems of equations. Indicate whether you used the y=mx+b method
or the intercept method to create your graph. Then state the coordinates of their intersection point.
Y=MX+B
(1) 𝑦 = 2𝑥 − 4
𝑦 = 𝑥+2
INTERCEPT
Y=MX+B
(2) 2𝑥 + 2𝑦 = 4
𝑥+𝑦=3
INTERCEPT
Y=MX+B
(3) 3𝑥 − 2𝑦 = 6
6𝑥 − 4𝑦 = 12
INTERCEPT
PRACTICE
Solve each system of equations algebraically. Circle the name of the method you chose.
Then explain how your solution relates to its graph.
SUBST.
(4) 𝑦 = 2𝑥 − 4
𝑦 = 𝑥+2
COMBO.
SUBST.
(5) 2𝑥 + 2𝑦 = 4
𝑥+𝑦 = 3
COMBO.
HOW DOES YOUR SOLUTION RELATE
TO ITS GRAPH ABOVE?
SUBST.
(6) 3𝑥 − 2𝑦 = 6
6𝑥 − 4𝑦 = 12
COMBO.
HOW DOES YOUR SOLUTION RELATE
TO ITS GRAPH ABOVE?
HOW DOES YOUR SOLUTION RELATE
TO ITS GRAPH ABOVE?
PRACTICE
Solve each system of equations algebraically. Circle the name of the method you chose.
Then explain why you chose that method.
SUBST.
COMBO.
PRACTICE
(7) 21𝑥 − 7𝑦 = 7
𝑦 = 3𝑥 − 1
WHY DID YOU CHOOSE THAT METHOD?
SUBST.
COMBO.
Consider the system:
WHY DID YOU CHOOSE THAT METHOD?
SUBST.
COMBO.
(9) 2𝑥 = 𝑦 + 4
−6𝑥 + 3𝑦 = −18
WHY DID YOU CHOOSE THAT METHOD?
(10) What can you do
to make this system
easier to solve?
𝑦= 𝑥−
𝑦=
(8) 2𝑥 + 𝑦 = 13
5𝑥 − 2𝑦 = 1
𝑥+
(12) In the space
at right, show
how to check your
solution algebraically.
(11) What is the solution to the system?
PRACTICE
Solve each
system of equations.
Indicate the method
you chose.
SUBST.
COMBO.
(13) 3𝑥 − 𝑦 = 7
𝑥+ 𝑦=2
CHECK:
SUBST.
COMBO.
(14) 𝑥 = −4𝑦
𝑥−𝑦 =6
Let 𝑓(𝑥) = √𝑥 + 7 and 𝑔(𝑥) = 3𝑥 − 27.
REVIEW
(15) 𝑔(−1) =
(16) 𝑓(−3) =
(17) 𝑓(−11) =
(18) 𝑔 𝑓(2) =
(19) 𝑓 𝑓(74) =
(20) If 𝑔(𝑥) = 0, then x=
(21) If 𝑓(𝑥) = 5, then x=
(22) Circle all of the inputs that are not valid inputs for the function 𝑓(𝑥).
3
—8
—20
10
7
—6
1
—7
—4
0
(23) Why are those inputs invalid?
REVIEW
Solve each inequality. Graph your results on a number line.
(24) |1 − 2𝑥| < 15
REVIEW
(25) 2|3𝑥 − 5| > 20
(26) −5|2𝑥 − 1| + 10 ≥ 5
Let 𝑓(𝑥) = 𝑥 + 1, 𝑔(𝑥) = 4𝑥 − 1, and ℎ(𝑥) = 6𝑥. Perform each operation.
(27) 𝑓(𝑥) + ℎ(𝑥)
(28) 𝑔(𝑥) ∙ ℎ(𝑥)
(29) 𝑓 ℎ(𝑥)
(30) 𝑔 ℎ(𝑥)
REVIEW
Factor each trinomial.
(31) 𝑥 − 𝑥 − 2
(32) 2𝑥 + 5𝑥 + 2
(33) 𝑥 − 6𝑥 − 55
(34) 𝑥 + 12𝑥 + 36
(35) 16𝑥 + 8𝑥 + 1
(36) 2𝑥 − 6𝑥 − 80