Question

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.

Answer 1

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!!!

Answer 2

-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