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(PLEASE HELP TYSM) Identify which variable to isolate, then solve for the variable and set up an equation containing one variable using substitution. Do not solve your final equation.

(PLEASE HELP TYSM) Identify which variable to isolate, then solve for the variable-example-1
User Cristiano Coelho
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1 Answer

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Problem 1 (on the left)

We can solve for y in the second equation since the coefficient here is 1.

Having coefficients that aren't -1 or 1 means we'd likely end up with fractions.

Add 5x to both sides like so:

y - 5x = 19

y = 5x+19

Now plug this into the first equation.

-3x - 8y = 20

-3x - 8( y ) = 20

-3x - 8( 5x+19 ) = 20

At this point, we have only one variable.

We stop here because your teacher does not want you to solve the final equation.

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Answers:

Variable to isolate: y

It leads to y = 5x+19 after solving the second equation for y.

And further leads to -3x - 8( 5x+19 ) = 20 after substitution.

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Problem 2 (on the right)

This time we can solve for x in the second equation. The reasoning is the same (coefficient of 1). Subtract 3y from both sides to get:

x+3y = 1

x = -3y+1

Substitute this into first equation.

Everywhere you see an x, replace it with -3y+1.

-3x - 3y = -15

-3( x ) - 3y = -15

-3( -3y+1 ) - 3y = -15

Like before, we now have one variable left.

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Answers:

Variable to isolate: x

It leads to x = -3y+1 when you solve for x in the second equation.

And further leads to -3( -3y+1 ) - 3y = -15 after substitution.

User Matt Schwartz
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