Final answer:
To solve the system of equations using elimination, we multiply the equations by appropriate constants to eliminate one variable, then solve for the remaining variable.
Step-by-step explanation:
To solve the system of equations using elimination, we want to eliminate one variable by adding or subtracting the equations. In this case, we can multiply the first equation by 2 and the second equation by -3, so that the coefficients of y will be the same but with opposite signs. When we add the new equations together, the y variable will be eliminated.
Multiplying the first equation by 2: 8x + 6y = -10
Multiplying the second equation by -3: -24x - 12y = 18
Adding the new equations together: -16x = 8
Solving this equation for x, we get x = -0.5. Substituting this value back into one of the original equations, we can solve for y. Using the first equation: 4(-0.5) + 3y = -5. Simplifying this equation, we get -2 + 3y = -5. Solving for y, we get y = -1.
Therefore, the solution to the system of equations is x = -0.5 and y = -1.