Find the solution of the system of equations.
minus, 2, x, minus, 3, y, equals, minus, 28
−2x−3y=
−28
minus, 2, x, plus, 2, y, equals, 22
−2x+2y=
22
To solve the system of equations, we can use the method of substitution or elimination.
Using the method of substitution, we solve one equation for one variable and substitute that expression into the other equation.
From the first equation, we have:
-2x - 3y = -28
-3y = 28 - 2x
y = (28 - 2x)/(-3) (equation 1)
Substituting this expression for y into the second equation, we have:
-2x + 2((28 - 2x)/(-3)) = 22
Multiplying both sides of the equation by -3 to remove the fraction, we get:
6x - 6(28 - 2x) = -66
6x - 168 + 12x = -66
18x - 168 = -66
18x = 102
x = 102/18
x = 17/3 or 5.67 (rounded to two decimal places)
Substituting this value of x back into equation 1 to solve for y, we have:
y = (28 - 2(17/3))/(-3)
y = (28 - 34/3)/(-3)
y = (84/3 - 34/3)/(-3)
y = 50/9 or approximately 5.56 (rounded to two decimal places)
Therefore, the solution to the system of equations is x = 5.67 and y = 5.56.