Find the solution of the system of equations.
15, x, minus, 4, y, equals, minus, 50
15x−4y=
−50
3, x, minus, 2, y, equals, minus, 16
3x−2y=
−16
To solve the system of equations, we can use the method of substitution.
First, we solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:
3x - 2y = -16
3x = 2y - 16
x = (2y - 16)/3
Then, we substitute this expression for x into the first equation:
15x - 4y = -50
15((2y - 16)/3) - 4y = -50
(30y - 240)/3 - 4y = -50
10y - 80 - 12y = -50
-2y - 80 = -50
-2y = 30
y = -15
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the second equation:
3x - 2(-15) = -16
3x + 30 = -16
3x = -16 - 30
3x = -46
x = -46/3
Therefore, the solution to the system of equations is x = -46/3 and y = -15.