Final answer:
To solve the system of equations using the elimination method, multiply the equations by appropriate coefficients to make the coefficients of one of the variables equal. Then, subtract one equation from the other to eliminate one variable. Solve for the remaining variable and substitute its value back to find the other variable. The solution to the system of equations is x = 2.72 and y = 4.95.
Step-by-step explanation:
To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying the equations by appropriate coefficients so that the coefficients of one of the variables become equal in both equations.
Multiply the first equation by 8 and the second equation by 12 to make the coefficients of x equal:
96x - 56y = -16 and 96x - 132y = 360
Subtract the second equation from the first equation to eliminate x:
(96x - 56y) - (96x - 132y) = -16 - 360
-76y = -376
Solve for y:
y = 4.95
Now substitute the value of y back into one of the original equations to find x:
12x - 7(4.95) = -2
12x - 34.65 = -2
12x = 32.65
x = 2.72
Therefore, the solution to the system of equations is x = 2.72 and y = 4.95.