# Math Expressions Worksheet With Answers - Grade 7 And 8 - University Of Waterloo - 2013 Page 7

7.
8
2x = 2
8.
x + 10 = 2(x
6)
8
2x+2x
=
2+2x
x +
10+12
= 2x
12+12
8
2
= 2 + 2x
2
x + 22
x
= 2x
x
6
2x
22 = x
=
2
2
Matt is 22.
3 = x
Exercises IV
Solve for x. Show all of your steps.
(a) x + 3 = 2
(b) 2
x =
3
(c)
3x + 7 =
8
x
(d)
+ 5 = 7
10
(e) 2
x + 8
y =
x + y + 3
2
x
10
9
(f)
+ 1 =
x
4
Solving Systems of Equations
Amanda has two fair options at the toy shop.
(1) She can buy one deck of Pok´ e mon cards and one Rubik’s Cube for \$20.
(2) Or for \$7, she can buy two decks of Pok´ e mon cards but she also has to trade in the
Rubik’s Cube she has at home.
What are the prices of a deck of Pok´ e mon cards and a Rubik’s Cube?
How can you solve this problem?
Notice that we have two unknowns: the price of a deck of Pok´ e mon cards (x) and the price
of a Rubik’s Cube (y). We also have two diﬀerent options that can be represented by two
diﬀerent equations:
(1) one deck + one cube = \$20. Mathematically, 1x + 1y = 20.
(2) two decks = \$7 + one cube. Mathematically, 2x = 7 + 1y or 2x
1y = 7.
The goal in this situation is to ﬁnd x and y such that both equations are satisﬁed.
A System of Equations is a set of multiple equations dealing with multiple variables. You
have to work with all of the equations at the same time in order to solve for the variables.
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