anonymous
  • anonymous
Solve using the substitution method. 5x − 7y = −16, 2x + 8y = 26
Mathematics
jamiebookeater
  • jamiebookeater
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Mertsj
  • 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
  • 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
  • anonymous
Ok mertsj I am still confused

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Mertsj
  • Mertsj
Can you divide the second equation by 2?
Mertsj
  • Mertsj
|dw:1327112923657:dw|
anonymous
  • anonymous
Ok I got that part
Mertsj
  • Mertsj
Now subtract 4y from both sides.
anonymous
  • anonymous
so 4y-y7 and 13-4y
Mertsj
  • Mertsj
|dw:1327113113852:dw|
Mertsj
  • Mertsj
So do you know how to substitute that in the other equation?
anonymous
  • anonymous
somewhat
Mertsj
  • Mertsj
Do you play a sport?
Mertsj
  • Mertsj
A team sport?
anonymous
  • anonymous
no
Mertsj
  • Mertsj
Do you watch sports on tv?
anonymous
  • anonymous
no sorry
Mertsj
  • 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
  • anonymous
would you divide the other side by 2 as weel
anonymous
  • anonymous
well*
Mertsj
  • Mertsj
|dw:1327113311498:dw|
Mertsj
  • Mertsj
Do you understand what I just did?
anonymous
  • anonymous
somewhat
Mertsj
  • Mertsj
Now use the distributive property and collect like terms
anonymous
  • anonymous
now math is my worst subject how do you do that
Mertsj
  • Mertsj
5(13-4y)=65-20y
Mertsj
  • Mertsj
Do you get that?
anonymous
  • anonymous
now how did you get that
Mertsj
  • Mertsj
The 5 outside the parentheses means to multiply everything in the parentheses by 5.
anonymous
  • anonymous
ok
Mertsj
  • Mertsj
So I multiplied 5 by 13 and got 65. Then I multiplied -4y by 5 and got -20y
Mertsj
  • Mertsj
Now -20y and -7y are like terms and they should be combined.
anonymous
  • anonymous
ok got that
anonymous
  • anonymous
so would it be 27y
Mertsj
  • Mertsj
Now subtract 65 from both sides.
Mertsj
  • Mertsj
It's actually -27y
Mertsj
  • Mertsj
|dw:1327113544265:dw|
anonymous
  • anonymous
ok got that part
Mertsj
  • Mertsj
Now divide both sides by -27
anonymous
  • anonymous
so would it be -27y/-27y and -16/-27y
Mertsj
  • Mertsj
|dw:1327113866037:dw|
Mertsj
  • Mertsj
Did you subtract 65 from BOTH SIDES?
anonymous
  • anonymous
yes I did than what do I do
Mertsj
  • Mertsj
So what do you have now? Then I can tell you what to do next.
anonymous
  • anonymous
this is all I have down
Mertsj
  • Mertsj
Do you have -27y=-81 ?
anonymous
  • 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
  • Mertsj
So yes. y=3.
Mertsj
  • Mertsj
x=13-4y so replace y with 3 and find x
Mertsj
  • Mertsj
x=13-4(3) x=13-12 x=1
anonymous
  • anonymous
ok and that how both of them end
Mertsj
  • Mertsj
-27y/-27y=-81/-27 That is a step you did. You should have divided by -27 and NOT by y just -27
anonymous
  • anonymous
oh ok
Mertsj
  • 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
  • anonymous
ok but its just says solve so I don't have to graph it right
Mertsj
  • 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
  • anonymous
oh ok great thank you so much you really helped
Mertsj
  • Mertsj
yw
anonymous
  • anonymous
have a good night
Mertsj
  • Mertsj
You too.

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