Please help. Topic: Criterias

Question

Given the system below, create an equivalent system and solve both to prove they result in the same solution.

       

-x+4y=17

 3x-5y= -30

Answer 1

-x + 4y = 17

3x - 5y = -30

Multiply the first equation by 3 on both sides.

-3x + 12y = 51

3x - 5y = -30

Add them up to eliminate x. Let's find the y-value by dividing both sides by 7.

7y = 21 → y = 3

Substitute 3 for y to find the x-value.

-x + 4(3) = 17

-x + 12 = 17

-x = 5

x = -5

The solution point is @ (-5, 3).

Let's check our solution. 3(-5) - 5(3) = -15 - 15 = -30. That match the system of linear equations.