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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: 7*x* + 3*y* = 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.

4*x* + 7*y* - 3 = 45

4

2.

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

9*x* - 33*y* = 48

9

9(9) - 33(1) = 48

9 x 9 = 81

33 x 1 = 33

81 - 33 = 48

*x* = 9

*y* = 1

Answer (d) is the correct answer

9 x 9 = 81

33 x 1 = 33

81 - 33 = 48

Answer (d) is the correct answer

3.

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

45*x* + 12*y* = 366

45

45(6) + 12(8) = 366

45 x 6 = 270

12 x 8 = 96

270 + 96 = 366

*x* = 6

*y* = 8

Answer (c) is the correct answer

45 x 6 = 270

12 x 8 = 96

270 + 96 = 366

Answer (c) is the correct answer

4.

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

8*x* - 2*y* = 52

8

8(8) - 2(6) = 52

8 x 8 = 64

2 x 6 = 12

64 - 12 = 52

*x* = 8

*y* = 6

Answer (c) is the correct answer

8 x 8 = 64

2 x 6 = 12

64 - 12 = 52

Answer (c) is the correct answer

5.

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

2*x* + 9*y* + 21 = 56

2

2(4) + 9(3) + 21 = 56

2 x 4 = 8

9 x 3 = 27

8 + 27 = 35

35 + 21 = 56

*x* = 4

*y* = 3

Answer (a) is the correct answer

2 x 4 = 8

9 x 3 = 27

8 + 27 = 35

35 + 21 = 56

Answer (a) is the correct answer

6.

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

12*x* + 20*y* = 108

12

12(4) + 20(3) = 108

12 x 4 = 48

20 x 3 = 60

48 + 60 = 108

*x* = 4

*y* = 3

Answer (b) is the correct answer

12 x 4 = 48

20 x 3 = 60

48 + 60 = 108

Answer (b) is the correct answer

7.

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

6*x* + 19*y* + 26 = 138

6

6(6) + 19(4) + 26 = 138

6 x 6 = 36

19 x 4 = 76

36 + 76 = 112

112 + 26 = 138

*x* = 6

*y* = 4

Answer (b) is the correct answer

6 x 6 = 36

19 x 4 = 76

36 + 76 = 112

112 + 26 = 138

Answer (b) is the correct answer

8.

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

5*x* + 5*y* - 10 = 55

5

5(6) + 5(7) - 10 = 55

5 x 6 = 30

5 x 7 = 35

30 + 35 = 65

65 - 10 = 55

*x* = 6

*y* = 7

Answer (c) is the correct answer

5 x 6 = 30

5 x 7 = 35

30 + 35 = 65

65 - 10 = 55

Answer (c) is the correct answer

9.

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

25*x* + 16*y* - 64 = 171

25

25(3) + 16(10) - 64 = 171

25 x 3 = 75

16 x 10 = 160

75 + 160 = 235

235 - 64 = 171

*x* = 3

*y* = 10

Answer (a) is the correct answer

25 x 3 = 75

16 x 10 = 160

75 + 160 = 235

235 - 64 = 171

Answer (a) is the correct answer

10.

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

3*x* + 9*y* = 36

3

3(6) + 9(2) = 36

3 x 6 = 18

9 x 2 = 18

18 + 18 = 36

*x* = 6

*y* = 2

Answer (d) is the correct answer

3 x 6 = 18

9 x 2 = 18

18 + 18 = 36

Answer (d) is the correct answer

The next step is:

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4 x 5 = 20

7 x 4 = 28

20 + 28 = 48

48 - 3 = 45

x= 5y= 4Answer (b) is the correct answer