Final answer:
By using the elimination method, we find that the value of the variable x in the solution to the system of equations 4x - 3y = 3 and 5x - 4y = 3 is x = 3.
Step-by-step explanation:
To determine the value of the variable x in the solution to the system of equations 4x - 3y = 3 and 5x - 4y = 3, we can use the method of substitution or elimination. Since the question does not provide an explicit preference, let's use the elimination method, as it directly addresses solving for x.
First, let's arrange the equations so they are in standard form.
- Equation 1: 4x - 3y = 3
- Equation 2: 5x - 4y = 3
Let's multiply the first equation by 4, and the second one by 3, to eliminate y from the equations.
- (4)×4x - (3)×4y = 3×4
- (5)×3x - (4)×3y = 3×3
We get:
- 16x - 12y = 12
- 15x - 12y = 9
Subtract the second equation from the first to solve for x:
16x - 12y - (15x - 12y) = 12 - 9
This simplifies to: x = 3