5x + 5y = 140
3x + 9y = 162
What is the solution for the system of equations above?
Responses
A x = 12, y = 16x = 12, y = 16
B x = 16, y = 12x = 16, y = 12
C x = 13, y = 15x = 13, y = 15
D x = 15, y = 13
To solve the system of equations, we can use either substitution or elimination. Let's use elimination method in this case.
First, we can multiply the first equation by 3 and the second equation by 5 to make the coefficients of x in both equations the same:
15x + 15y = 420
15x + 45y = 810
Next, we subtract the first equation from the second equation:
15x + 45y - (15x + 15y) = 810 - 420
30y = 390
Now we can solve for y:
y = 390/30
y = 13
Substituting y back into the first equation to solve for x:
5x + 5(13) = 140
5x + 65 = 140
5x = 75
x = 15
Therefore, the solution for the system of equations is x = 15, y = 13. The correct answer is D.