Question

Need checking on this problem MEDAL + FAN Please!

Solve the system of equations by substitution.

x=-4y
x+5y=2

(-8,2)
(8,-2)
(2/9,8/9)
(-12,3)

Answer 1

I think it is 8,-2

Answer 2

Did you just guess, or did you solve the system?

Answer 3

I tried to work it out but I just estimated based on what I got I am a little confused...

Answer 4

That solution happens to be incorrect.
I can show you how to solve the system using substitution.

Answer 5

Yes, please!

Answer 6

In the substitution method, you first need to have one of the equations solved for one variable.
In this system notice that the first equation is already solved for x, since the equation reads x = something.

Answer 7

The first step of the substitution method is to solve one of the equations for one variable.
That step is already done for us in this problem.

Now we go to the next step in the substitution method.
The second step in the substitution method is to substitute the variable that is solved for in the other equation.

Answer 8

Okay

Answer 9

The first equation tells us that x is the same as -4y.
Now we take the second equation, and everywhere we see x, we substitute it with -4y.

The second equation is:
x + 5y = 2

Substitute -4y in for x:

-4y + 5y = 2

Do you follow so far?

Answer 10

Now the second equation has only one variable, y.
We can solve it for y.

-4y + 5y = 2

y = 2

Answer 11

Now that we found that y = 2, we again substitute to find x.

We can use either of the two original equations, so let's use the first one since it's simpler.

x = -4y

x = -4(2)

x = -8

The solution is (-8, 2)

Answer 12

Thank you so much!

Answer 13

You're welcome.
Be sure you understand the steps in the substitution method.

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The substitution method of solving a system of 2 equations in 2 variables
1. Solve one equation for one variable.
2. Substitute what that variable is equal to in the other equation.
3. Solve for the remaining variable.
4. Substitute the known variable in one of the original equations, and solve for the other variable.
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