[substitution method][section 28]

(1.) x = y + 4

2x - 5y = 2 here is the problem

2(y + 4) - 5y = 2 replace x with y + 4

2y + 8 - 5y = 2 multiply thru parentheses

-3y + 8 = 2 combine like terms

3y - 8 = -2 multiply thru by -1

+8 +8 add 8 to each side
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3y = 6 add
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3 3 divide each side by 3

y = 2 divide and cancel

x = 2 + 4 replace y with 2

x = 6 add

result: x = 6 and y = 2

(2.) y = 3 - x

5x + 3y = -1 here is the problem

5x + 3(3 - x) = -1 replace y with 3 - x

5x + 9 - 3x = -1 multiply thru parentheses

2x + 9 = -1 combine like terms

-9 -9 subtract 9 from each side
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2x = -10 subtract
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2 2 divide each side by 2

x = -5 divide and cancel

y = 3 - (-5) replace x with -5

y = 8 add

result: x = -5 and y = 8

(3.) x = 8y

x - 4y = 12 here is the problem

8y - 4y = 12 replace x with 8y

4y = 12 combine like terms
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4 4 divide each side by 4

y = 3 divide and cancel

x = 8(3) replace y with 3

x = 24 multiply

result: x = 24 and y = 3

(4.) 5x - y = 1

3x + 2y = 11 here is the problem

-5x + y = -1 multiply equation 1 thru by -1

+ 5x + 5x add 5x to each side
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y = 5x - 1 add

3x + 2(5x - 1) = 11 replace y with 5x - 1

3x + 10x - 2 = 11 multiply thru parentheses

13x - 2 = 11 combine like terms

+ 2 + 2 add 2 to each side
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13x = 13 add
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13 13 divide each side by 13

x = 1 divide and cancel

y = 5(1) - 1 replace x with 1

y = 4 multiply & combine like terms

result: x = 1 and y = 4


(5.) 5a = b

a = 10b - 49 here is the problem

a = 10(5a) - 49 replace b with 5a

a = 50a - 49 multiply

-a = -50a + 49 multiply thru by -1

+50a +50a add 50a to each side
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49a = 49 add
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49 49 divide each side by 49

a = 1 divide and cancel

b = 5(1) replace a with 1

b = 5 multiply

result: a = 1 and b = 5


(6.) r = 5 - s

2r + 7s = 20 here is the problem

2(5 - s) + 7s = 20 replace r with 5 - s

10 - 2s + 7s = 20 multiply thru parentheses

10 + 5s = 20 combine like terms

-10 -10 subtract 10 from each side
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5s = 10 subtract
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5 5 divide each side by 5

s = 2 divide and cancel

r = 5 - 2 replace s with 2

r = 3 subtract

result: r = 3 and s = 2

(7.) 4x - y = 15

5x - 8y = -15 here is the problem

-4x + y = -15 multiply equation 1 thru by -1

+4x + 4x add 4x to each side
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y = 4x - 15 add

5x - 8(4x - 15) = -15 replace y with 4x - 15

5x - 32x + 120 = -15 multiply thru parentheses

-27x + 120 = -15 combine like terms

27x - 120 = 15 multiply thru by -1

+120 +120 add 120 to each side
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27x = 135 add
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27 27 divide each side by 27

x = 5 divide and cancel

y = 4(5) - 15 replace x with 5

y = 5 multiply and combine like terms

result: x = 5 and y = 5

(8.) r + s = 3

r - s = 1 here is the problem

+ s + s add s to each side
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r = s + 1 add

s + 1 + s = 3 replace r with s + 1

2s + 1 = 3 combine like terms

-1 -1 subtract 1 from each side
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2s = 2 subtract
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2 2 divide each side by 2

s = 1 divide and cancel

r = 1 + 1 replace s with 1

r = 2 add

result: r = 2 and s = 1

(9.) p - 3q = 0

2p - 5q = 2 here is the problem

p - 3q = 0

+ 3q +3q add 3q to each side
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p = 3q add

2(3q) - 5q = 2 replace p with 3q

6q - 5q = 2 multiply

q = 2 combine like terms

p = 3(2) replace q with 2

p = 6 multiply

result: p = 6 and q = 2

(10.) 2a + b = 5

8a - b = -5 here is the problem

-8a + b = 5 multiply equation 2 thru by -1

+8a +8a add 8a to each side
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b = 8a + 5 add

2a + 8a + 5 = 5 replace b with 8a + 5

10a + 5 = 5 combine like terms

- 5 -5 subtract 5 from each side
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10a = 0 subtract
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10 10 divide each side by 10

a = 0 divide and cancel

b = 8(0) + 5 replace a with 0

b = 5 multiply & add

result: a = 0 and b = 5