Final answer:
To solve the system of equations x - 2y = 18 and 4x + 3y = -16, we can use the method of elimination. Multiply the first equation by 2 and the second equation by 3 to make the coefficients of y equal in both equations. Add the two equations together to obtain a new equation relating x and y. Solve this equation and substitute the value back into one of the original equations to find the other variable.
Step-by-step explanation:
To solve the system of equations x - 2y = 18 and 4x + 3y = -16, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the first equation by 2 to make the coefficients of y in both equations equal: 2(x - 2y) = 2(18) becomes 2x - 4y = 36.
Multiply the second equation by 3 to make the coefficients of y in both equations equal: 3(4x + 3y) = 3(-16) becomes 12x + 9y = -48.
Add the two equations together:
(2x - 4y) + (12x + 9y) = 36 + (-48)
14x + 5y = -12.
Now we have a new equation that relates x and y. We can solve this equation for either variable and substitute the value back into one of the original equations to find the other variable.
I hope this helps! Let me know if you have any further questions.