Question

PLEASE ANSWER ASAP!!! SHOW ALL THE STEPS.

Solve the system of equations using elimination. Make sure to show all work and find the value of both x and y

1.

x - 3y = 7

3x + 3y = 9

2.

8x+ 3y = 1

4x + 2y = 0

Answer 1

For the first question
`x = 4\\ y = -1` and

For the second question
`x = 0.5\\ y = -1`

Explanation:

Given:

1.

x - 3y = 7

3x + 3y = 9

2.

8x+ 3y = 1

4x + 2y = 0

Elimination method :

In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.

Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.

For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get

`(x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = (16)/(4)\\x = 4`

Now substitute X equal to 4 in equation x -3y = 7 we get

`4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = (3)/(-3)\\ y = -1\\`

This way we have x is equal to 4 and y is equal to -1 for question number 1.

For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get

`8x + 4y = 0\\`

Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get

`(8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1`

Now substitute y equal to -1 in equation 8x +3y = 1 we get

`8x + 3* -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = (4)/(8)\\ x = 0.5\\`

This way we have x is equal to 0.5 and y is equal to -1 for question number 2.