Question

What is the value of x in the solution to the system of linear equations? {y=3x+2 y=x-4 a –7 b –3 c 1 d 5

Answer 1

Since y must equal both 3x+2 and x-4, we deduce that 3x+2 and x-4 must equal each other. So, we have

`3x+2=x-4 \iff 2x+2=-4 \iff 2x=-6 \iff x=-3`

Answer 2

b. -3

Explanation:

the system is:

`y=3x+2\\y=x-4`

to find the value of x, we need to eliminate the y variable.

We can eliminate the 'y' by substracting the equations:

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

which is simplified to:

`0=2x+6`

and clearing for x:

`2x=-6\\x=-6/2\\x=-3`

which is option b.