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3x + 2y = -4,x + 2y = -8

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2 Answers

Hi Averie!

Let's go through this question one step at a time.  First, we have to remember what substitution means: solve for one variable with one equation, and then substitute this solution into the other equation.

We want to find which variable would be easiest to solve for.  Both equations have a coefficient (2) on the variable y.  The second equation does not have a coefficient for x.  This means it'll be easier to solve for x, so we'll go ahead and do that using the second equation.

x + 2y = -8  |Subtract 2y from both sides to get x alone
x +2y - 2y = -8 - 2y  
x = -8 - 2y

Now we have an equation for x!  Let's substitute it into the other equation (3x+2y = -4).

3x + 2y = -4  |Rewrite the equation
3 (-8 - 2y) + 2y = -4 |substitute for x
-24 -6y + 2y = -4  |distribute!
-24 -4y = -4  |combine terms
-24+24 -4y = -4+24  |add 24 to both sides
-4y = 20  
-4y / -4 = 20/-4  |divide by -4 on both sides
y = -5  |solve!

Now we know that y = -5, so we're ready to finish solving for x!  Remember that x= -8 - 2y, so let's plug in our value for y and find x!

x = -8 - 2y  |rewrite equation
x = -8 - 2(-5)  |substitute in y=-5
x = -8 + 10  |solve
x = 2

Our final answer is x=2, y=-5

Good luck!

Equation 1: 3x + 2y = -4

Equation 2: X + 2y = -8

To solve this question using substitution, we need to find a way to substitute one equation into the other so that we eliminate one of the variables from one equation. To do this, we can realize that there is a “2y” in each equation.

Step 1. Solve for 2y in equation 2.

X+2y = -8

-x          -x

--------------

2y = -8-x.

Step 2: Plug this into equation 1 for 2 y.

3x+ -8 – x = -4

Step 3: Simplify by combining like terms.

2x -8 = -4

+8       +8

--------------

2x = 4

/2   /2

X = 2

Now that x is known, just plug this number back into one of the equations and solve for y. You should find that y = -5.