Final answer:
To find the solution, we can eliminate one variable by multiplying an equation, then add the equations together to eliminate the same variable. Solve for the remaining variable and substitute it back to find the other variable.
Step-by-step explanation:
To find the solution to the system of equations:
5x - y = 10
3x - 2y = -1
- Multiply the second equation by 2 to eliminate the y variable: 6x - 4y = -2
- Add the modified second equation to the first equation: 5x - y + 6x - 4y = 10 + (-2)
- Simplify the combined equation: 11x - 5y = 8
- Use the result from step 3 to substitute and solve for x in the first equation: 11x - 5(103 - 5x) = 8
- Solve for x and substitute the value back into one of the original equations to find y.
The solution to the system of equations is x = 5 and y = 27.