What is the x coordinate of the solution to the system?

-2x+6y=-38

3x-4y=32

I tried both linear combination and substitution, but I can't eliminate any variables. I know I'm doing something wrong, but I don't know what.

We will solve this system with method of opposing coefficients - Gaussian algorithm

-2x+6y = - 38

3x-4y = 32

We will divide first equation with number 2 and get

-x+3y = - 19

then we will multiply the same equation with number 3 and get

-3x+9y = - 57

We will overwrite the second equation below the last one and get next equivalent system

-3x+9y = - 57

3x-4y = 32

We add first equation to the second and get

5y = - 25 = > y = - 25/5 = > y = - 5

Now we will replace variable y = - 5 in the equation - x+3y = - 19 and get

-x+3 (-5) = - 19 = > - x-15 = - 19 = > x - 19-15=4 = > x=4

The correct answer is (x, y) = (4,-5)

We can check in the first equation and get

-2*4+6 * (-5) = - 38

-8-30 = - 38

-38 = - 38 We get equality, the solutions are correct.

This system have one real solution.

Good luck!

-2x + 6y = - 38 ⇒ 3 (-2x + 6y = - 38) ⇒ - 6x + 18y = - 114

3x - 4y = 32 ⇒ 2 (3x - 4y = 32) ⇒ 6x - 18y = 64

0 = 50

FALSE

False statement means there are no solutions.

Answer: No Solution