How do you solve the following linear system 3 x-2y=4 , x+4y=3?

2 Answers
Feb 12, 2017

y = 5/14
x = 11/7

Explanation:

1) Rearrange your equations to make them easier to use. The easiest way to do this is to isolate ONE variable that has the coefficient of 1.

3x - 2y = 4

x = -4y + 3

2) Since you now know what the x variable is in terms of y, you can go ahead and substitute it into the first equation.

3 (-4y + 3) - 2y = 4

3) Simplify

3 (-4y + 3) - 2y = 4

-12y + 9 - 2y = 4

-14y + 9 = 4

-14y = -5

y = 5/14

4) Substitute the solution you just got to get the second variable.

x + 4y = 3

x + 4 (5/14) = 3

x + 10/7 = 3

x = 11/7

Feb 12, 2017

x=11/7=1 4/7 and y=5/14

Explanation:

3x-2y=4
x+4y=3

Using the second equation, derive a value for x.

x+4y=3

Subtract 4y from each side.

x=3-4y

In the first equation, substitute x with color(red)((3-4y)).

3x-2y=4

3color(red)((3-4y))-2y=4

Open the brackets and simplify. The product of a positive and a negative is a negative.

9-12y-2y=4

9-14y=4

Subtract 9 from each side.

-14y=-5

Divide both sides by -14.

y=5/14

In the second equation, substitute y with color(blue)(5/14).

x+4y=3

x+4(color(blue)(5/14))=3

Open the brackets and simplify.

x+2cancel4xx5/(7cancel14)=3

x+10/7=3

Subtract 10/7 from each side.

x=3-10/7

x=21/7-10/7

x=11/7=1 4/7