Find the solution of the system of equations.
minus, 5, x, minus, 6, y, equals, minus, 32
−5x−6y=
−32
4, x, minus, 6, y, equals, 4
4x−6y=
4
The given system of equations is:
-5x - 6y = -32
4x - 6y = 4
To solve this system, we'll use the method of substitution.
From the first equation, we can isolate x by subtracting 6y from both sides:
-5x = -32 + 6y
Dividing both sides by -5, we get:
x = (32 - 6y)/5
Now, substitute this value of x into the second equation:
4((32 - 6y)/5) - 6y = 4
Multiplying both sides by 5 to clear the fraction, we have:
4(32 - 6y) - 30y = 20
Distributing, we get:
128 - 24y - 30y = 20
Combining like terms, we have:
-54y = -108
Dividing both sides by -54, we get:
y = 2
Now substitute this value of y back into the expression for x:
x = (32 - 6(2))/5
x = (32 - 12)/5
x = 20/5
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 2.