Solve using the substitution method: x+y=7/2 and then under that 4x-3y=-14?

Answer 1

x + y = 7/2
4x - 3y = -14

From the first equation, x = 7/2 - y

Sub this in the second equation:
4( 7/2 - y) - 3y = -14

14 - 4y - 3y = -14
28 = 7y ...........................y = 4

Put this back in the first equation to find x:

x = (7/2 - 4) = -1/2

Check your work in the second equation:
4(-1/2) - 3(4) = -14
(-2) - (12) = -14..................Good!

Answer 2

x + y = 7/2- - - - - -Equation 1
4x - 3y = - 14- - - - -Equation 2
- - - - - - - - -

Substitute Method equation 1

x + y = 7/2

x + y - x = 3.5 - x

y = 3.5 - x

The answer is y = 3.5 -- x

Insert the y value into equation 2

- - - - - - - - - -

4x - 3y = - 14

4x - 3(3.5 - x) = - 14

4x - 10.5 + 3x = - 14

7x - 10.5 + 10.5 = - 14 + 10.5

7x = - 3.5

7x/7 = - 3.5/7

x = - 0.5

The answer is x = - 0.5

Insert the x value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

4x - 3y = - 14

4(- 0.5) - 3y = - 14

- 2 - 3y = - 14

- 2 - 3y + 2 = - 14 + 2

- 3y = - 12

- 3y /-3 = - 12 / - 3

y = 4

The answer is y = 4

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

Check for equation 2

4x - 3y = - 14

4(-0.5) - 3(4) = - 14

- 2 - 12 = - 14

- 14 = - 14

- - - - - - -

Check for equation 1

x + y = 7/2

- 0.5 + 4 = 3.5

3.5 = 3.5

- - - - - - - - -

The solution set is { - 0.5, 4 }

- - - - - - - - s-

Answer 3

The key to this is that you can't solve an equation with two unknowns, can you? So you have to get it down to one unknown.

Pick either they x or the y. Solve for it. Then plug in the answer for it into your variable in the other equation.

Example: x+ y = 1 and 2x + y = 5.

I'll solve the fist eq for x. x=1-y.

So now, in the other eq, I subsitute 1-y wherever I see x.
So in the second eq, I now have 2(1-y) + y =5.

Now I can solve for y! After that I can use one of the original eq's and the value I just got for y to solve for x.

Just apply that method to your equations!!! Good luck!

Answer 4

x+y = 7/2
x = 7/2-y

4x-3y = -14
4(7/2-y)-3y = -14
14-4y-3y = -14
-7y = -14-14
-7y = -28
7y = 28
y = 28/7
y = 4

x = 7/2-y
x = 7/2-4
x = 7/2-8/2
x = -1/2

Answer 5

x = -1/2
y = 4

Answer 6

y=7/2-x
4x-3(7/2-x)=-14
4x-21/2+3x=-14
7x=21/2-14
x=-3.5/7
x=-1/2

y=7/2-x
y=7/2+1/2
y=4