Final answer:
To find the solution to the system of equations 5x - 8y = -45 and 9x - 8y = 49, you can solve by elimination. The solution is x = 23.5 and y = 20.3125.
Step-by-step explanation:
To find the solution to the system of equations:
5x - 8y = -45
9x - 8y = 49
- Subtract the second equation from the first equation to eliminate y. This gives you 5x - 9x = -45 - 49, which simplifies to -4x = -94.
- Solve for x by dividing both sides of the equation by -4. This gives you x = -94/-4, or x = 23.5.
- Substitute the value of x into one of the original equations to solve for y. Using the first equation, we have 5(23.5) - 8y = -45. Simplifying this equation gives you 117.5 - 8y = -45.
- Subtract 117.5 from both sides of the equation to isolate -8y. This gives you -8y = -45 - 117.5, which simplifies to -8y = -162.5.
- Solve for y by dividing both sides of the equation by -8. This gives you y = -162.5/-8, or y = 20.3125.