Question

What is the solution of the system? Use the elimination method. {4x+2y=182x+3y=15 Enter your answer in the boxes.

Answer 1

x=3

y=3

Explanation:

Given :
`4x+2y=18\\2x+3y=15`

To solve : Solution of system of equation

Solution :

`4x+2y=18` ---(a)

`2x+3y=15` ---(b)

Since we are given that we have to solve these equation by elimination method :

Multiply equation (a) by 2 and equation (b) by 4

Then equation becomes:

`8x+4y=36` ---(a)

`8x+12y=60` ---(b)

Subtract (a) from (b)

`8x+12y-60-(8x+4y-36)=0`

`8x+12y-60-8x-4y+36=0`

`8y-24=0`

`y=(24)/(8)`

`y=3`

Now put this value in (b) to get value of x

`8x+12(3)=60`

`8x+36=60`

`8x=60-36`

`8x=24`

`x=(24)/(8)`

`x=3`

Thus the solution of this system of equations is x=3 and y=3

Answer 2

`\left \{ {{4x+2y=18(1)} \atop {2x+3y=15(2)}} \right.`
Lets multiply equation (2) by -2 to get:

`-4x-6y=-30`

Now we can add equations (1) and (2) to eliminate x:

`\left \{ {{4x+2y=18}+ \atop {-4x-6y=-30}} \right.`

`-4y=-12`

`y= (-12)/(-4)`

`y=3`
Now that we know the value of y, we can replace it in equation (1) to get the value of x:

`4x+2(3)=18`

`4x+6=18`

`4x=12`

`x= (12)/(3)`

`x=3`

We can conclude that both x and y are equal to 3.