Answer:
To solve the system of equations using the elimination method, we'll manipulate the equations to eliminate one variable.
Given equations:
1. 3y = 20 - 4c ...........(Equation 1)
2. 2y = 12 - 3x ...........(Equation 2)
Step 1: Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of y equal:
(2) * (3y = 20 - 4c) => 6y = 40 - 8c ...........(Equation 3)
(3) * (2y = 12 - 3x) => 6y = 36 - 9x ...........(Equation 4)
Step 2: Now, we have two equations with the same coefficient for y, so we can subtract Equation 4 from Equation 3 to eliminate y:
(6y = 40 - 8c) - (6y = 36 - 9x)
6y - 6y = 40 - 8c - 36 + 9x
0 = 4 - 8c + 9x
9x = 4 - 8c
x = (4 - 8c) / 9 ...........(Equation 5)
Step 3: Substitute the value of x from Equation 5 into Equation 2 to find y:
2y = 12 - 3x
2y = 12 - 3 * (4 - 8c) / 9
2y = 12 - (12 - 24c) / 9
2y = (108 - 12 + 24c) / 9
2y = (96 + 24c) / 9
y = (96 + 24c) / 9 * 1/2
y = (48 + 12c) / 9
y = (16 + 4c) / 3 ...........(Equation 6)
So, the solutions for the system of equations are:
x = (4 - 8c) / 9
y = (16 + 4c) / 3
Explanation: