Final answer:
To solve the system of equations using elimination, we can multiply both equations by constants to make the coefficients of one of the variables equal in magnitude but opposite in sign. By adding the resulting equations, we can solve for that particular variable. Substituting the value of that variable back into one of the original equations allows us to solve for the other variable. The solution to the given system of equations is (4, 6).
Step-by-step explanation:
To solve the system of equations using elimination, we want to eliminate one variable by multiplying one or both equations by a constant so that the coefficients of one variable will cancel when added/subtracted. Let's eliminate the y variable.
Multiply the first equation by 4 and the second equation by 6 to make the coefficients of y equal:
24y - 16x = 80
-24y + 18x = -72
Add the two equations:
2x = 8
Divide both sides by 2:
x = 4
Substitute the value of x into the first equation:
6y - 4(4) = 20
6y - 16 = 20
6y = 36
Divide both sides by 6:
y = 6
Therefore, the solution to the system of equations is (4, 6).