To solve this system of equations, we can use the method of substitution or elimination.
1) We will use the method of substitution to solve the system of equations 4x - 3y = 12 (equation 1 x + y = 45 (equation 2 y - 2x = 1 (equation 3 x - 6y = 4 (equation 4)
From equation 2, we can express x in terms of y x = 45 - y
To solve this system of equations, we can use the method of substitution or elimination.
1) We will use the method of substitution to solve the system of equations
4x - 3y = 12 (equation 1
x + y = 45 (equation 2
y - 2x = 1 (equation 3
x - 6y = 4 (equation 4)
From equation 2, we can express x in terms of y
x = 45 - y
Substitute x = 45 - y into equations 1, 3, and 4:
4(45 - y) - 3y = 1
180 - 4y - 3y = 1
-7y = -16
y = 24
x = 45 - 24 = 21
Therefore, the solution is x = 21, y = 24.
2) Now let's check the solution in the remaining equations:
x + y = 4
21 + 24 = 45, the equation is satisfied.
y - 2x =
24 - 2(21) =
24 - 42 =
-18 = 1, this equation is not satisfied.
x - 6y =
21 - 6(24) =
21 - 144 =
-123 = 4, this equation is also not satisfied.
Therefore, the solution x = 21, y = 24 does not satisfy all the equations, so there may be an error in the calculations.