Question

What is the value of the x variable in the solution to the following system of equations?

3x + y = 1
6x + 2y = −9

0

2

There is no x value as there is no solution to this system

x can be any value as there are infinitely many solutions to this system

Answer 1

do you prefer substitution or elimination ?

Answer 2

Substitution.

Answer 3

3x + y = 1 --> y = -3x + 1
now sub -3x + 1 in for y in the 2nd equation
Can you do that ?

Answer 4

Let me get you started...
6x + 2y = -9
6x + 2(-3x + 1) = -9
can you take it from here and solve for x ?

Answer 5

What exactly do I do now?

Answer 6

you distribute the 2 through the parenthesis....can you do that ?

Answer 7

I don't know what you mean.

Answer 8

let me show you...
6x + 2(-3x + 1) = -9
6x - 6x + 2 = -9
do you see what I did ?

Answer 9

No.

Answer 10

ok....
6x + 2(-3x + 1) = -9
we want to get rid of the parenthesis. To do this,we have to multiply the number right outside of the parenthesis, with everything in the parenthesis.
6x + 2 * -3x + 2*1 = -9
are you with me so far ?

Answer 11

Yes.

Answer 12

then we get : 6x - 6x + 2 = -9
understanding ?

Answer 13

Yeah.

Answer 14

we then want to move the 2 to the other side by subtracting 2 from both sides...like this
6x - 6x + 2 - 2 = -9 - 2
I subtracted 2 from both sides and now the equation reads :
6x - 6x = -11
do you understand ?

Answer 15

Yeah.

Answer 16

6x - 6x = -11
0 = -11
when you have an equation where the end results do not equal, that means there is no solution.
If the equation would have ended like this : 2 = 2 or 7 = 7, where it would equal, then there would be infinite solutions. Or if it would have ended like this: x = 4 or x = 6 then there would be one solution. So this system of equations has no solutions. Do you have any questions ?

Answer 17

No questions. Thank you.

Answer 18

your welcome...glad I could help :)