Question

Use the elimination method to solve the following system of equations.

4x - 12y = 0
x + 3y = 7

Answer 1

x= 7/2 y = 7/6

Explanation:

4x - 12y = 0

x + 3y = 7

Multiply the second by( -4) to eliminate the X variable

4x - 12y = 0

-4x -12y= -28

ADD BOTH

-24y=-28

Divide both by -24

y= 28/24

y=7/6

Plug y into second equation

x + 3y = 7

x+ 3(7/6) = 7

x+21/6=7

x+7/2=7

x=7-(7/2)

x=( 14/2) - (7/2)

x= 7/2

Answer 2

For this case we have the following system of equations:

`4x-12y = 0\\x + 3y = 7`

To solve, we follow the steps below:

We multiply the second equation by -4:

`-4x-12y = -28`

We add the equations:

`4x-4x-12y-12y = 0-28`

Equal signs are added and the same sign is placed.

`-24y = -28\\y = \frac {-28} {- 24}\\y = \frac {14} {12} = \frac {7} {6}`

We look for the value of the variable "x":

`x = 7-3y\\x = 7-3 \frac {7} {6}\\x = 7- \frac {21} {6}\\x = \frac {42-21} {6}\\x = \frac {21} {6}\\x = \frac {7} {2}`

Thus, the solution of the system is:

`(x, y): (\frac {7} {2}; \frac {7} {6})`

Answer:

`(x, y): (\frac {7} {2}; \frac {7} {6})`