Final answer:
To solve the system of equations -3x - 5y = -7 and -4x + 5y = 14 using elimination, add the equations together to cancel out the y terms, then solve for x and substitute that value back into one of the original equations to find y. The solution is x = 1 and y = 0.8.
Step-by-step explanation:
To solve the system of equations using elimination, we combine the equations -3x - 5y = -7 and -4x + 5y = 14. Notice that the y terms have opposite coefficients, so when added together, they will cancel each other out.
Step 1: Add the two equations directly to eliminate the y terms.
- -3x - 5y = -7
- -4x + 5y = 14
Adding these together gives:
- -3x - 5y + (-4x + 5y) = -7 + 14
- -7x = 7
Step 2: Solve for x:
Step 3: Substitute x = 1 back into either original equation to find y:
- -3(1) - 5y = -7
- -5y = -7 + 3
- -5y = -4
- y = -4 / -5
- y = 4/5 or 0.8
The solution to the system of equations is x = 1 and y = 0.8. After finding the solution, always check to ensure it satisfies both original equations.