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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

Respuesta :

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

[tex]3x+2=x-4 \iff 2x+2=-4 \iff 2x=-6 \iff x=-3[/tex]

Answer:

b. -3

Step-by-step explanation:

the system is:

[tex]y=3x+2\\y=x-4[/tex]

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

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

[tex]y=3x+2\\-(y=x-4)\\-----------\\y=3x+2\\-y=-x+4\\------------\\y-y=3x-x+2+4[/tex]

which is simplified to:

[tex]0=2x+6[/tex]

and clearing for x:

[tex]2x=-6\\x=-6/2\\x=-3[/tex]

which is option b.

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