Solve the system of equations.%0D%0A6x–5y=27%0D%0A6%0D%0A%0D%0A–%0D%0A5%0D%0A%0D%0A=%0D%0A27%0D%0A%0D%0A3x+5y=36%0D%0A3%0D%0A%0D%0A+%0D%0A5%0D%0A%0D%0A=%0D%0A36%0D%0A(1 point)%0D%0A(, )

Answer 1

To solve the system of equations, we can use the method of substitution or elimination.

Using substitution:
From the first equation, we can isolate x:
6x - 5y = 27
6x = 5y + 27
x = (5y + 27)/6

Substituting this value of x into the second equation:
3(5y + 27)/6 + 5y = 36
Multiply both sides by 6 to eliminate the denominator:
3(5y + 27) + 30y = 216
15y + 81 + 30y = 216
45y + 81 = 216
45y = 135
y = 135/45
y = 3

Substituting y = 3 back into the first equation to find x:
x = (5(3) + 27)/6
x = (15 + 27)/6
x = 42/6
x = 7

Therefore, the solution to the system of equations is (x, y) = (7, 3).