Use the Substitution method to solve the system of equations.?

Question

Use the Substitution method to solve the system of equations.

x + y = 20
30x + 25y = 550

show work please

Answer 1

x + y = 20- - - - - - - -- -Equation 1
30x + 25y = 550- - - - Equation 2
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Substitute Method equation 1

x + y = 20

x + y - x = - x + 20

y = - x + 20

substitute the y value into equation 2

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30x + 25y = 550

30x + 25( - x + 20) = 550

30x +(- 25x + 500) = 550

30x - 25x + 500 = 550

5x + 500 = 550

5x + 500 - 500 = 550 - 500

5x = 50

5x / 5 = 50 / 5

x = 50 / 5

x = 10

Insert the x value into euation 1

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x + y = 20

10 + y = 20

10 + y - 10 = 20 - 10

y = 10

Insert the y value into equation 1

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Check for equation 1

x + y = 20

10 + 10 = 20

20 = 20

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Check for equation 2

30x + 25y = 550

30(10) + 25(10) = 550

300 + 250 = 550

550 = 550

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The two equations balance

The solution set is {10. 10 }

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Answer 2

x + y = 20
30x + 25y = 550

30x + 25(20 - x) = 550
5x = 50
x = 10 so y = 10 also.

Answer 3

Take either equation and solve for either x or y:

x+y = 20
x = 20 - y

Plug this value for x into the other equation:

30(20 - y) + 25y = 550
600 - 30y + 25y = 550
600 - 5y = 550
-5y = -50
y = 10

Put the value for y back into the first equation:

x + 10 = 20
x = 10

X = 10, y = 10

Answer 4

y=20-x
30x+25(20-x)=550
30x+500-25x=550
5x=50
x=10
y=20-10=10