Question

How do I solve this linear system using the elimination method?

x+4y=14


3x-2y=7

Answer 1

Solution:
`x=4`,
`y = (5)/(2)`

Explanation:

System of Equations

Solve the system:

x + 4y = 14

3x - 2y = 7

using the elimintation method.

To use the elimination method, we must add or subtract both equations in such a way that one of the variables goes away, and only one remains.

It requires to multiply one of them by a specific factor to match the coefficients. For example, multiply the first equation by -3:

-3x - 12y = -42

And add it to the second:

3x - 2y = 7

To result:

-14y = -35

Divide by -14:

`y = -35/(-14)`

Simplifying:

`y = (5)/(2)`

Now calculate x:

`x = 14 - 4*(5)/(2)`

`x = 14-10`

`x=4`

Solution:
`x=4`,
`y = (5)/(2)`