Solve each system using substitution. y+6=2x 4x-10y=37

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nick-teal eNotes educator| Certified Educator



To solve a system of equations, first we solve for a variable (x or y) in one equation, and then plug it into the other equation.

We will solve the first equation for y.

`y + 6 = 2x`

`y + 6 - 6 = 2x - 6`

`y = 2x - 6`

Now that we know what y equals in the first equation, we plug it into the second to solve for x.

`4x - 10y = 37`

`4x - 10(2x - 6) = 37`

`4x - 20x + 60 = 37`

`-16x + 60 = 37`

`-16x + 60 - 60 = 37 - 60`

`-16x = -23`

`x = 23/16`

Now that we have solved for x, we can plug it in to either equation to figure out what y is.

`y = 2x - 6`

`y = 2(23/16) - 6`

`y = 23/8 - 6`

`y = -25/8`

We solved for y in terms of x in the first equation, plugged it into the second equation to find the true value of x.  Then used that value to find out what y is.

`x = 23/16`

atyourservice | Student



The first step is to solve one of the problems, y+6=2x seems easier to solve so i'll go with that first:

y + 6 = 2x

y = 2x - 6

Now plug in y as the y on the other problem:

`4x - 10(2x-6) = 37`

Now distribute the -10

`4x - 20x + 60 = 37`

combine like terms

`-16x = -23`

divide by -16

x = 23/16 or 1.4375 ( the negative disappeared because both numbers are negative therefore cancelling it out)

Now that we have x, plug it in as the x in any of the 2 problems to find y:



`y + 6 =2.87500`

subtract 6

y =  -3.12500

deepm | Student

First we need to solve for either x or y in order to use the substitution method.

Lets solve the first equation to simplify for y as the subject then we can use it for the second equation to find the value for x.


To simplify y we need to get rid of the +6 

we know its +6 so we will do the opposite to both the sides.

It will look something like this..


when we simplify this equation it becomes : y= 2x-6

Now, we will use this equation to substitute in the second equation : 4x-10y=37

4x- 10 (2x-6) = 37

4x- 20x+60=37

-16x= 37-60


x= 23/16

After simplifying we now know the value of x= 23/16

Now  plug in the value into the 1 simplified equation : y= 2x-6

y= 2(23/16) -6

y=23/8 -6

y= -3.125 or -25/8

shonasharma | Student

just begin by saying... it's a piece of cake!

ok, so write your equations:

1.  y+6=2x

2.  4x-10y=37

Then, you simply chose an easy equation from the two provided, in which you can make either x or y the subject of the formula.

In this question, the first equation is simpler: y+6=2x where you should make y the subject.

When making it the subject, read  out loud all that is before the equal sign. it's y+6. after saying y, u say +6, so in order to make y the subject, quickly say the opposite( minus 6). write that down on the left hand side of the equal sign as well as the right hand side of it:


Then cancel the -6 and +6 from the left hand side.

It then becomes:


Tadda! you have made y the subject.

Now, do what your eyes tell you to do: 

your equation says that y=2x-6 now and your second equation reads


Now, when you see your second equation, you leave 4x as it is. But when you move ahead with subtracting 10y from it, you actually see y beside your 10( which means y is being multiplied by 10).

Write the second equation again:

4x-but this time as soon as you write 10, take a look at both the need to put y....what is your y, take a deep look at the equation where you made y the subject.


Hence, if your y is 2x-6, just write down your second equation as :


Now, do what you see

-write down 4x

-then expand using binomial expansion:

   -10 x 2x  gives you -20x.........and then, -10 x -6 gives you +60

write your equation as such:


bring 37 on the left side and equate the whole side to 0: is important to note that when switching sides, change the sign.inthe above the right hand side was +37 but when you take it to the left, it changes to -37.

so, collect your like terms.

4x and 20x seem like like terms, so just operate on your patient! do 4x-20x which will give you -16x.

Then, do, +60-37 which gives you +23.

Now, you will have -16x+23=0 in front of you.

Just find x now.

read out load to find x, if it says -16x+23 before equal sign, do the opposite on both sides:


cancel the -23 and +23 on the left hand side:


read from x again, it says x multiplied by -16, so do the opposite and divide it by -16 on both sides:

-16x/-16 =-23/-16

on the left, you are left with x and on the right is -23/-16.

so, your x is -23/-16.

To find y:

again use a simpler equation. you can even use the one in which you made y the subject which was:


do, y =2(-23/-16)-6

multiply 2 by your bracket first and then from that answer, subtract 6.

you should get -3 1/8 or -3.125

so your y is -3.125.

do make sure to put your figured out x and y values in both the original equations to see if they are correct.


(-3.125)+6 should give you 2(-23/-16)



4(-23/-16) - 10(-3.125) should give you 37.

sorry if it's too long:) but I hope you understand.