Solve using the substitution method?

Question

This one is stumping me, big time !
Solve using the substitution method -
x = 4y-2
x = 6y+8

Answer 1

x = 4y-2
x = 6y+8

Take what X equals from the first equation and simply "plug" it into the second equation.

4y-2=6y+8

Now, get the Y's on one side of the equation, plain numbers on the other side.

-10=2y

Solve for Y and X

Y = -5
X = -22

Answer 2

Substitue 4y-2 or 6y+8 into one of the equations, whichever one you choose will be fine because it will be the same equation no matter what, just backwards.
I'll try to simplify it more:

eq. 1) x=4y-2 eq. 2) x=6y+8
Substitute either 4y-2 or 6y+8 into the other equation.
If you use 4y-2 from eq. 1, eq. 2 would now look like this:
4y-2=6y+8 because if x is 4y-2, you can just put it right into where the x is in eq. 2 - because x IS 4y-2.

It is the same for if you use 6y+8 from eq. 2 -- x IS 6y+8 so you can put this phrase into equation one where the x is because 6y+8 equals x. It would look like this - 6y+8=4y-2

Then after you have either 6y+8=4y-2 or 4y-2=6y+8, you can solve for y by adding together like terms.
Using 4y-2=6y+8......
Add the 4y and 6y together by subtracting 4y from the positive 4y on the left side of the equal sign and by 6y to get 2y on the right side of the equal sign : 4y-2=6y+8
-4y -4y
^ the +4y and -4y cancels out leaving...
-2=2y+8
you are trying to get y by itself, so you need to subtract 8 from the positive 8 on the right side and subtract 8 from the negative 2 on the left to get -10 on the left: -2=2y+8
-8 -8
^ the +8 and - 8 cancels out leaving....
-10=2y
To get y by itself, you need to divide the 2y by 2 (do the opposite to cancel the 2 out, like we did when it was addition/subtraction), and divide the -10 by 2: -10=2y
-10/2=2y/2
^the multiplied 2 and divided 2 cancels out leaving....
-5=y <--- -5 IS y ---- So now that you have y, you can put in -5 in either eq.1 or 2 and solve : (using eq 1):

x = 4y-2
x = 4(-5)-2
x = -20-2
x = -22 ! So the ordered pair to solve these equations is
(x, y) : (-22, -5)

Answer 3

SIMPLE using x=4y-2, put this in place of x in the other equation
4y-2 = 6y + 8.

Now get all x terms to one side and constant terms to the other side thus 4y -4y -2 -8 = 6y +8 -8 -4y this becomes

-10 = 2y , thus y = -5 now since y = -5 then x = 4 ( -5) -2 or

x = -22

Answer 4

Take the second equation and substitute 4y-2 in place of x

4y-2 = 6y+8

Bring the like terms at one place
4y-6y = 8+2
-2y=10 ==> y=-5

now substitute the value of y in equation one

x=4y-2 ==> 4(-5) -2 ==> -22

So the x =-22 and y=-5

Answer 5

Hi,

The problem is kindda already set you up to set both equations equal to each other. Notice that both equations are equal to the same variable; "x". Therefore, we can set them equal and follow the following steps:

4y - 2 = 6y + 8

Add 2 to both sides of the equation . . .

4y = 6y + 10

Subtract 6y from both sides of the equation . . .

-2y = 10

Divide both sides by -2 to get y = -5.

Notice that we now know that y = -5 and we can use any one of the given equation to find x by substituting y = -5.

x = 4 ( - 5) - 2

x = - 20 - 2

x = - 22

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 6

You already have the first equation solved for x, so replace x in the second equation with this value. You get:
4y - 2 = 6y + 8

This simplifies to
-2 = 2y + 8
-10 = 2y
y = -5

Now plug this y value into either of the original equations to solve for x. You've now solved for both variables.

Answer 7

x = 4y - 2
x = 6y + 8

x - 4y = - 2
x - 6y = 8

change the signs in 2nd eqn.

2y = -10
y = -5

substitute in 1st eqn.

x = 4(-5) - 2
x = -20 -2
x = -22

Answer 8

Since x=4y-2 and x=6y+8, we can conclude that

4y-2=6y+8

-2y=10

y=-5
x=-22

The only solution is (-22,-5).

Answer 9

6y + 8 = 4y - 2
2y = - 10
y = - 5
x = - 20 - 2
x = - 22
Solution is x = - 22 , y = - 5

Answer 10

6y+8 = 4y-2
6y+10 = 4y
(6y+10) / 4 = y