Question

Use addition to solve the linear system of equations. Include all of your work in your final answer. 3x-y=6 and y=x-4

Answer 1

x = 1 and y = -3

Explanation:

The given linear equations are,

3x - y = 6 and y = x - 4

To solve the system of equations

Let 3x - y = 6 -----(1)

y = x - 4

x - y = 4 ----(2)

(2) * -3 ⇒ -3x + 3y = -4 ----(3)

(2) + (3) ⇒

3x - y = 6

-3x + 3y = -12

0 +2y = -6

y = -6/2 = -3

x - y = 4

x = 4 + y = 4 + -3 = 1

x = 1 and y = -3

Answer 2

x = 1, y = -3

Explanation:

So, we have two equations to start with: 3x-y=6 and y = x-4, we want to resolve the equations by addition.

We sum up the left sides of the equations together and the right sides together, and simplify, we have:

3x - y + y = 6 + x - 4

3x = 2 + x ==> 2x = 2 ==> x = 1

To find y, we place the value of x in any of the two equations:

y = x - 4 = 1 - 4 = -3

You verify that the solution is valid by entering the values of x and y in the other equation:

3x - y = 6 becomes

3 (1) - (-3) = 6

3 + 3 = 6