Final answer:
To solve the system of equations, use the method of elimination. Multiply the second equation by 2 to make the coefficients match, then add the equations to eliminate the x term. Solve for y by substituting the value of x back into either of the original equations.
Step-by-step explanation:
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination. We can start by multiplying the second equation by 2 to make the coefficients of y equal:
2x + y = 20
-12x + 10y = 24
Now, we can add the two equations together:
(2x + y) + (-12x + 10y) = 20 + 24
-10x + 11y = 44
Simplifying further:
11y = 10x + 44
y = (10/11)x + 4
Now we can substitute this value of y into either of the original equations to find the value of x. Let's use the first equation:
2x + y = 20
2x + (10/11)x + 4 = 20
(22/11)x + (10/11)x = 16
(32/11)x = 16
x = 16 * (11/32)
x = 5.5
Substituting this value of x back into the equation for y:
y = (10/11) * 5.5 + 4
y = 5 + 4
y = 9
So the solution to the system of equations is x = 5.5 and y = 9.