Find the solution of the system of equations.
minus, 3, x, plus, 8, y, equals, 11
−3x+8y=
11
minus, 3, x, minus, 5, y, equals, minus, 41
−3x−5y=
−41
To solve the system of equations, we can use the method of elimination.
Writing the equations in standard form:
-3x + 8y = 11 (Equation 1)
-3x - 5y = -41 (Equation 2)
To eliminate the variable x, we need to multiply Equation 2 by -1:
-3x + 8y = 11 (Equation 1)
3x + 5y = 41 (Equation 3)
Adding Equation 1 and Equation 3 together:
(-3x + 8y) + (3x + 5y) = 11 + 41
13y = 52
Dividing both sides of the equation by 13:
y = 52/13
y = 4
Substitute the value of y back into Equation 1:
-3x + 8(4) = 11
-3x + 32 = 11
Subtracting 32 from both sides of the equation:
-3x = 11 - 32
-3x = -21
Dividing both sides of the equation by -3:
x = -21/-3
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 4.