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

To find the value of the x variable in the given system of equations, use the substitution method to solve for x.

Step-by-step explanation:

To find the value of the x variable in the given system of equations:

2x - 3y = 3

5x - 4y = 4

We can solve the system by using the method of substitution or elimination. Let's use the method of substitution:

1. From the first equation, isolate x by adding 3y to both sides: 2x = 3 + 3y
2. Divide both sides of the equation by 2 to solve for x: x = (3 + 3y) / 2
3. Substitute this expression for x in the second equation:
4. 5((3 + 3y) / 2) - 4y = 4
5. Simplify the equation: (15 + 15y) / 2 - 4y = 4
6. Multiply both sides of the equation by 2 to eliminate the fraction: 15 + 15y - 8y = 8
7. Combine like terms: 15y - 8y = 8 - 15
8. Simplify: 7y = -7
9. Divide both sides of the equation by 7 to solve for y: y = -1
10. Substitute this value of y back into the expression for x: x = (3 + 3(-1)) / 2
11. Simplify: x = (3 - 3) / 2
12. Simplify further: x = 0

Therefore, the value of the x variable in the solution to the given system of equations is 0.