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solve with substitution. answer as ordered pair. 3x-y=66 2y=x

{algebra math substitution} please hellppp mee i have 5 questions that are really hard for me and I have tried them every way i can think of and each time its the wrong answer and I cant just put the correct answer even though I know it (because my teacher posted them online so we can check it at home and not have to waste time in class) because we have to show our work and if I can't show the work that got me to that correct answer i get it wrong. I have done 32 problems on my own already, but these five are really stumping me! please help me!

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3 Answers

This is a system of equations which means that they each have the same solution for x and y.

If 3x-y=66 and if x=2y

then you can write that

3(2y)-y=66   (everytime you see x in the first equation you can write 2y)

then solve for y

6y-y=66

5y=66

y=13.2

Now you know what y is   13.2

so you can put 13.2 anywhere you see y in either equation to get x

3x-13.2=66

3x=79.2

x=26.4

also

2(13.2)=x

26.4=x

(x,y)

(26.4,13.2)

Substitution means that you take one equation and put the variables in terms of each other, then you substitute that value in for the other variable in the remaining equation.

Since there are two equations in two variables you can substitute 4 total ways.

Using your equations:

3x - y = 66    Equation 1

2y = x           Equation 2

Looking at equation 2, you already have x in terms of y, so substitute 2y in place of x in equation 1:

3(2y) - y = 66

6y - y = 66

5y = 66

y = 66/5

Now substitute that value in the equation 2

2(66/5) = x

132/5 = x

(132/5, 66/5) is your answer

Use both values in equation 1 to check:

3(132/5) - (66/5) = 66

396/5 - 66/5 = 66

Multiply both sides by 5

5*(396/5) - 5*(66/5) = 66*5

396 - 66 = 330

330 = 330

So our solutions hold.

This time using equation 1:

3x - y = 66

3x - 66 = y

2(3x - 66) = x

6x - 132 = x

5x = 132

 x = 132/5

Substituting that into equation 1:

3(132/5) - y = 66

396/5 - y = 66

Multiplying through by 5 again

396 - 5y = 330

396 - 330 = 5y

66 = 5y

66/5 = y