how do you solve this by the substitution method: y = -2x + 3 and 3x - 2y = 8?

Answer 1

3x - 2(3 - 2x) = 8
3x - 6 + 4x = 8
7x = 14
x = 2

y = - 4 + 3
y = - 1

x = 2 , y = - 1

Answer 2

First, let's substitute y=2x+8 into the first equation. Replace all instances of "y" in the first equation with "2x+8" We have 3x-2(2x+8)=2 Distribute the -2 to each term inside of the parentheses. 3x-2(2x)-2(8)=2. This will simplify to 3x-4x-16=2. Now let's isolate the x variable on one side to get a value. We'll start by combining the x terms. A positive 3x and a negative 4x make a negative 1x, so let's fill that in: -x-16=2 Add 16 to both sides of the equation. -x=18 Finally, multiply both sides of the equation by -1. x=-18 Now that we have an x value, let's plug that in to the second equation. Replace all instances of x with "-18". y=2(-18)+8 Multiply the 2 and the -18 to get -36. Adding an 8 to this gives a -28. y=-28

Answer 3

x=2 y= -1 .... you have to put the y= -2x+3 into 3x-2y=8 so it looks like this 3x-2(-2x+3)=8 you solve that get x=2 then you plug in the answer for x which is 2 to either equations it will look like this..
y= -2(2)=3 then you get y= -1!

Answer 4

The first equation is already solved for y, so plug it into the second equation and solve for x:

3x - 2(-2x + 3) = 8
3x - (-4x + 6) = 8
7x - 6 = 8
7x = 14
x = 2

Then plug the 2 into the first equation and solve for y:
y = -2(2) + 3
y = -4 + 3
y = -1

Finally, plug the values for x and y into the second equation as a check:

3(2) - 2(-1) = 8
6 - (-2) = 8
6 + 2 = 8
8 = 8 --> Check!

Answer 5

The first equation tells you that y=-2x+3

In the second equation, substitute this expression for y whenever y appears, so the second equation becomes:

3x -2(-2x+3)=8
3x+4x-6=8
7x = 14
x=2
y=-2x+3=-2(2)+3=-1

Check:
-1=-2(2)+3 ok
3(2)-2(-1)=6+2=8 ok

Answer 6

put the value of y= -2x + 3 in the second equation.

you will then get something like

3x + 4x -6=8

then solve for x

Answer 7

Sub the value of y from the first equation into the second:
3x - 2y = 8
3x - 2 (-2x + 3) = 8

Now solve for x:
3x + 4x - 6 = 8
3x + 4x = 8 + 6
7x = 14
x = 2

Now use this value of x to solve for y. Sub x = 2 into either equation. I'll sub into the first equation:
y = -2x + 3
y = -2(2) + 3
y = -1

Hope this helps :)

Answer 8

y = -2x + 3
3x - 2y = 8
Substitute for y in second equation.
3x - 2(-2x+3) = 8
Remove brackets:
3x +4x - 6 = 8
7x = 14
x = 2

Answer 9

Matrices are obviously way beyond your scope, and plus you only use matrices when the system of equations are big and complicated.

you substitute y=-2x+3 into the other equation:

3x-2(-2x+3)=8
3x +4x -6 = 8
7x =14
x=2

then you take the x=2 and substitute it back into the first eqn.
y=-2(2) + 3 = -4 +3
y=-1

Answer 10

put the y in the 2y just like this
3x-2(-2x + 3)=8
3x+4x+6=8
7x+6=8
7x=8-6
7x=2 then you need to divide 7divide by 7it will turn to x because they are cancel then 2 divided by 7 is .28 or you can say 2 over 7thats when you got the x next you need to get the y
y=-2(.28)+3
y= -.56+3
y=2.44
then you got your y intersept so you just need to show your points like this
(.28,2.44) or (2/7,2.44) than you got your subtitution method: