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

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nick-teal's profile pic

nick-teal | High School Teacher | (Level 3) Adjunct Educator

Posted on

y+6=2x

4x-10y=37

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's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

y+6=2x

4x-10y=37

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=2x`

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

`y + 6 =2.87500`

subtract 6

y =  -3.12500

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deepm | Student, Undergraduate | eNotes Newbie

Posted on

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.

y+6=2x

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..

y+6-6=2x-6

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

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's profile pic

shonasharma | Student, Undergraduate | (Level 1) eNoter

Posted on

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:

y+6-6=2x-6

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

It then becomes:

y=2x-6

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

4x-10y=37.

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 equations...you need to put y....what is your y, take a deep look at the equation where you made y the subject.

y=2x-6

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

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

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:

4x-20x+60=37

bring 37 on the left side and equate the whole side to 0:

4x-20x+60-37=0........it 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:

-16x+23-23=0-23

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

-16x=-23

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:

y=2x-6

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.

y+6=2x

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

and

4x-10y=37

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

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

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