Question

What is the solution to the system of linear equations? {2x+4y=203x+2y=26 enter your answer in the boxes. ( , )?

Answer 1

(3,4) is the answer, with x=3 and y=4

Answer 2

`(8,1)`

Explanation:

We have been given a system of linear equations:

`2x+4y=20...(1)`

`3x+2y=26...(2)`

We will use substitution method to solve linear equation. From equation (1) we will get,

`x=(20-4y)/(2)`

Substituting this value in equation (2) we will get,

`3*(20-4y)/(2)+2y=26`

`(60-12y)/(2)+2y=26`

Let us have a common denominator.

`(60-12y)/(2)+(2*2y)/(2)=26`

`(60-12y)/(2)+(4y)/(2)=26`

`(60-12y+4y)/(2)=26`

`(60-8y)/(2)=26`

`(60-8y)/(2)*2=26*2`

`60-8y=52`

`60-60-8y=52-60`

`-8y=-8`

Upon dividing both sides by
`-8` we will get,

`(-8y)/(-8)=(-8)/(-8)`

`y=1`

Upon substituting
`y=1` in equation (1) we will get,

`2x+4*1=20`

`2x+4=20`

`2x+4-4=20-4`

`2x=16`

Upon dividing both sides of the equation by 2 we will get,

`(2x)/(2)=(16)/(2)`

`x=8`

Therefore, the solution of our given system of equations is
`(8,1)`.