Question

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

2x − 3y = 3
5x − 4y = 4

A. −1

B. 0

C. x can be any number as there are infinitely many solutions to this system

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

Answer 1

Do you know how to solve simultaneous equations by elimination? If not, would you like me to show you the general technique?

Answer 2

Show me how please.

Answer 3

Take equation #1 and multiply both sides by "-5". This will give you an new equation #1. Multiply both sides of equation #2 by "2" for a new equation #2. The reason you are doing this is that you will then add the left side of the new equation #1 to the left side of the new equation #2 (same for the right sides) and you want one of the variables to cancel out. In this case, the "x" variable will cancel out. Go ahead and try that now.

Answer 4

Starting with the new equation #1, what does that look like? Please write that out here.

Answer 5

Hint: the coefficient on "x" in the new equation #1 will be "-10". The coefficient on "x" in the new equation #2 will be "+10". When you add -10 x to +10x, you will get "zero x". The sum of both sides of the new equations will produce an equation where the "x" term will disappear.

Answer 6

Are you able to do this, or are you stuck?

Answer 7

@Viceroy ?

Answer 8

New equation #1:

(-5)(2x − 3y) = (-5)(3)
-10x + 15y = -15

New equation #2:

(2)(5x − 4y) = (2)(4)
10x - 8y = 8

Adding corresponding sides:

-10x + 15y = -15
10x - 8y = 8
-----------------------
(0)x +7y = -7
y = -1

Going back to the first equation (substituting for "y"):

2x − 3(-1) = 3
2x + 3 = 3
2x = 0
x = 0

Answer 9

Ok, @viceroy , that's a full explanation and shows that x = 0.

Answer 10

Alternatively, you can solve for x in equation 1 and slot the values into equation 2. Then solve for y in the new equation 2 (which is -1) then slot the y value into the ORIGINAL equation one and solve for x which in this case is 0. :)