Question

Use addition to solve the linear system of equations. Include all of your work in your final answer. \(\left\{ \right.\) 3x-y=6 y=x-4

Answer 1

Solving the given linear system, we get x = 1 and y = -3.

The solution set is: (1,-3)

Explanation:

We need to solve the linear system of equations.

`3x-y=6 \\y=x-4`

We can write second equation y=x-4 as:
`-x+y=-4`

Let:

`3x-y=6--eq(1)\\ -x+y=-4--eq(2)`

Now, Adding equation 1 and 2

`3x-y=6\\ -x+y=-4\\--------\\2x+0y=2\\2x=2\\x=(2)/(2)\\x=1`

So, we get x = 1

Now, put value of x in second equation to find value of y:

`y=x-4\\Put\:x=1\\y=1-4\\y=-3`

So, we get y = -3

Solving the given linear system, we get x = 1 and y = -3.

The solution set is: (1,-3)