SOLUTION:
Case: System of equations
Given: A pair of equations
Required: To solve the equation by finding the values of (x, y)
Method:
Step 1: First we simplify both equations
Equation 1
− ( + ) = ( − ) +
x - 12y -21 = 4 -2y +4x
Collecting like terms
-21-4 = 4x -x -2y +12y
-25 = 3x +10y
3x + 10y = -25...............equation (1)
Equation 2
( + ) + ( + ) = −1
6x +24 +20y + 15 = -11
Collecting like terms
6x + 20y = -11 -20-15
6x - 20y = -46
Dividing through by 2
3x - 10y = -23...............equation (2)
Step 2:Use elimination method to solve the equation pair
Equation (1) - (2)
(3x- 3x)+ (10y - (-10y)) = -25 - (-23)
10y + 10y = -25 + 23
20y = -2
Dividing both sides by 20
y= -2/ 20
y= -0.1 OR -1/10
Step 3: Plug y= -0.1 int equation (2)
3x - 10y = -23
3x - 10(-0.1) = -23
3x +1 = -23
3x = -23 -1
3x = -24
Dividing both sides by 3
x= -8
Final answer:
The value of x= -8 and y= -0.1. (-8, -0.1)