How do you solve the system x+2y=13 and 3x-5y=6 using substitution?

1 Answer
Fabio
Mar 17, 2018

x=7
y=3

Explanation:

So you can pick either one of the 2 equations listed to get 1 term alone. In explanation I will be using the second one (3x-5y=6)

So we have 3x-5y=6

First we add 5y to both sides giving us
3x=5y+6

Next we divide 3 on both sides to get x alone, which gives us
x=5/3y+6/3

x=5/3y+2

Now that have x we can plug this into the first equation, which is (x+2y=13)

5/3y+2+2y=13

Now we subtract the 2 on both sides giving us
5/3y+2y=11

Now we add the y values by finding common denominators
5/3y+"(3)2"/"(3)1"y=11

Then add the y values
5/3y+6/3y=11

(5y+6y)/3=11

(11y)/3=11

Now we multiply by 3 on both sides
11y=33

Next divide by 11
y=3

So now that we have the value for y we can find x easily by plugging this into any equation that has y. For this part I'm going to use the first equation which was, x+2y=13

y=3
x+2y=13

x+2(3)=13

x+6=13

Subtracting 6 from both sides gives us
x=7

There fore
x=7
y=3

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