Question

A system of equations is given equation one: 3y=20-4c euestion two: 2y=12-3x solve for (x,y) using the elimination method show all work

Answer 1

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: