Solve using the substitution method.
5x − 7y = −16, 2x + 8y = 26

- anonymous

Solve using the substitution method.
5x − 7y = −16, 2x + 8y = 26

- jamiebookeater

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- Mertsj

Divide the second equation by 2 and solve it for x
You will get x=13-4y
Put that into the first equation in place ofx

- anonymous

i would use the 2nd equation to substitute because the numbers are more simple.
get down to x =( )
so 2x +8y = 26
2x = 26 -8y
x = (26 - 8y)/2
x = 13 -4y
now you can replace this x into the other equation
5x - 7y = -16
replace the x
5(13 - 4y) - 7y = -16
65 - 20y - 7y = -16
solve for y
-27y = -71
y = 3
replace y=3 into any equation to find x
2x + 8y = 26
2x + 8(3) = 26
2x + 24 = 26
2x = 2
x =1
y = 3

- anonymous

Ok mertsj I am still confused

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## More answers

- Mertsj

Can you divide the second equation by 2?

- Mertsj

|dw:1327112923657:dw|

- anonymous

Ok I got that part

- Mertsj

Now subtract 4y from both sides.

- anonymous

so 4y-y7 and 13-4y

- Mertsj

|dw:1327113113852:dw|

- Mertsj

So do you know how to substitute that in the other equation?

- anonymous

somewhat

- Mertsj

Do you play a sport?

- Mertsj

A team sport?

- anonymous

no

- Mertsj

Do you watch sports on tv?

- anonymous

no sorry

- Mertsj

Well I thought you might know what it means when the coach substitutes one player for another. Any way, we have to take that name for x that we just found and replace x with it.

- anonymous

would you divide the other side by 2 as weel

- anonymous

well*

- Mertsj

|dw:1327113311498:dw|

- Mertsj

Do you understand what I just did?

- anonymous

somewhat

- Mertsj

Now use the distributive property and collect like terms

- anonymous

now math is my worst subject how do you do that

- Mertsj

5(13-4y)=65-20y

- Mertsj

Do you get that?

- anonymous

now how did you get that

- Mertsj

The 5 outside the parentheses means to multiply everything in the parentheses by 5.

- anonymous

ok

- Mertsj

So I multiplied 5 by 13 and got 65. Then I multiplied -4y by 5 and got -20y

- Mertsj

Now -20y and -7y are like terms and they should be combined.

- anonymous

ok got that

- anonymous

so would it be 27y

- Mertsj

Now subtract 65 from both sides.

- Mertsj

It's actually -27y

- Mertsj

|dw:1327113544265:dw|

- anonymous

ok got that part

- Mertsj

Now divide both sides by -27

- anonymous

so would it be -27y/-27y and -16/-27y

- Mertsj

|dw:1327113866037:dw|

- Mertsj

Did you subtract 65 from BOTH SIDES?

- anonymous

yes I did than what do I do

- Mertsj

So what do you have now? Then I can tell you what to do next.

- anonymous

this is all I have down

- Mertsj

Do you have
-27y=-81 ?

- anonymous

5x − 7y = −16
5(13-4y)-7y=-16
5(13-4y)=65-20y
65-20y-7y=-16
-20y+-7y=-27y
65-27y=-16
-65 -65
-----------
-27y/-27y=-81/-27
y=3
2x/2 + 8y/2 = 2b/2
x + 4y = 13
-4y -4y
x=13-4y

- Mertsj

So yes. y=3.

- Mertsj

x=13-4y so replace y with 3 and find x

- Mertsj

x=13-4(3)
x=13-12
x=1

- anonymous

ok and that how both of them end

- Mertsj

-27y/-27y=-81/-27
That is a step you did. You should have divided by -27 and NOT by y just -27

- anonymous

oh ok

- Mertsj

So yes. The solution is x = 1 and y = 3 which is the ordered pair (1,3) And if you would graph those equations, the two lines would cross at the point (1,3)

- anonymous

ok but its just says solve so I don't have to graph it right

- Mertsj

That's right. You don't have to graph it. I just wanted you to know the connection between the solution of the system and the graph.

- anonymous

oh ok great thank you so much you really helped

- Mertsj

yw

- anonymous

have a good night

- Mertsj

You too.

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