 The letter X is commonly used as a variable.

# Pre-Algebra - Variables

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Algebra comes with a whole new set of terminology to learn. One of those terminologies is that of a monomial. A monomial is a polynomial that has only one term. So what is a polynomial?

A polynomial is an expression of variables and coefficients. The variables and coefficients involve mathematical operations that include addition, subtraction, multiplication and non-negative integer-exponents.

So, what is a variable? A variable is an alphabetic character used to represent a number that is not known. For example: x + y. The “x” and “y” are variables used in place of numeric numbers that are not known.

What is a coefficient? A coefficient is a known number that is linked to a variable. For example: 7x + 3y = 29. In this example the 7 and the 3 are coefficients because they are linked to variables. The 29 is a constant number and is not a coefficient because it is not linked to a variable.

Whenever a coefficient is linked to a variable, it is understood that the operation will be multiplied. Again looking at the above example, we know that 7 times an unknown number plus 3 times an unknown number will equal 29. When replacing a variable with a number, the number is placed within parentheses. Now let’s look at the solution to our problem as it should be written out.

7(2) + 3(5) = 29
7 x 2 = 14
3 x 5 = 15
14 + 15 = 29
x = 2
y = 5

1.
For the problem below, determine the correct value of the variables.

12x + 20y = 108
x = 3,y = 4
x = 4, y = 3
x = 2, y = 5
x = 5, y = 3
12(4) + 20(3) = 108
12 x 4 = 48
20 x 3 = 60
48 + 60 = 108
x = 4
y = 3
2.
For the problem below, determine the correct value of the variables.

45x + 12y = 366
x = 7, y = 3
x = 5, y = 7
x = 6, y = 8
x = 3, y = 9
45(6) + 12(8) = 366
45 x 6 = 270
12 x 8 = 96
270 + 96 = 366
x = 6
y = 8
3.
For the problem below, determine the correct value of the variables.

4x + 7y - 3 = 45
x = 4, y = 5
x = 5, y = 4
x = 3, y = 6
x = 2, y = 7
4(5) + 7(4) - 3 = 45
4 x 5 = 20
7 x 4 = 28
20 + 28 = 48
48 - 3 = 45
x = 5
y = 4
4.
For the problem below, determine the correct value of the variables.

3x + 9y = 36
x = 2, y = 3
x = 7, y = 1
x = 3, y = 2
x = 6, y = 2
3(6) + 9(2) = 36
3 x 6 = 18
9 x 2 = 18
18 + 18 = 36
x = 6
y = 2
5.
For the problem below, determine the correct value of the variables.

25x + 16y - 64 = 171
x = 3, y = 10
x = 3, y = 9
x = 4, y = 7
x = 5, y = 5
25(3) + 16(10) - 64 = 171
25 x 3 = 75
16 x 10 = 160
75 + 160 = 235
235 - 64 = 171
x = 3
y = 10
6.
For the problem below, determine the correct value of the variables.

9x - 33y = 48
x = 11, y = 2
x = 7, y = 1
x = 10, y = 2
x = 9, y = 1
9(9) - 33(1) = 48
9 x 9 = 81
33 x 1 = 33
81 - 33 = 48
x = 9
y = 1
7.
For the problem below, determine the correct value of the variables.

8x - 2y = 52
x = 9, y = 8
x = 7, y = 5
x = 8, y = 6
x = 8, y = 7
8(8) - 2(6) = 52
8 x 8 = 64
2 x 6 = 12
64 - 12 = 52
x = 8
y = 6
8.
For the problem below, determine the correct value of the variables.

2x + 9y + 21 = 56
x = 4, y = 3
x = 3, y = 5
x = 4, y = 2
x = 5, y = 3
2(4) + 9(3) + 21 = 56
2 x 4 = 8
9 x 3 = 27
8 + 27 = 35
35 + 21 = 56
x = 4
y = 3
9.
For the problem below, determine the correct value of the variables.

6x + 19y + 26 = 138
x = 5, y = 3
x = 6, y = 4
x = 8, y = 2
x = 7, y = 3
6(6) + 19(4) + 26 = 138
6 x 6 = 36
19 x 4 = 76
36 + 76 = 112
112 + 26 = 138
x = 6
y = 4
10.
For the problem below, determine the correct value of the variables.

5x + 5y - 10 = 55
x = 8, y = 4
x = 5, y = 6
x = 6, y = 7
x = 8, y = 6
5(6) + 5(7) - 10 = 55
5 x 6 = 30
5 x 7 = 35
30 + 35 = 65
65 - 10 = 55
x = 6
y = 7