The given problem is an application of 2 linear equation.
In mathematics, linear equation define as any equation that can be written in the standard form of ax + b = 0. where a and b are real numbers.
Given:
Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1
a.) By graphing
The value of x and y of the two equation is where the two line intersect.
To graph, let x = 0, and y = 0 to get to dots, then connect the two dots
x = 0
2x - 3y = -1
0 - 3y = -1
y = 1/3 → (0,1/3)
y = 0
2x - 3y = -1
2x - 0 = -1
x = -1/2 → (-1/2,0)
Graph the line 2x-3y=-1 using (-1/2,0) and (0,1/3).
For y = x-1
let x = 0
y = x-1
y = 0-1
y = -1 → (0,-1)
let y = 0
y = x-1
0 = x -1
x = 1 → (1,0)
Graph the line using (0,-1) and (1,0).
Base from the graph, the line intersect in (4,3),
therefore x = 4 and y = 3.
b.) Elimination
Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1
2x - 3y = -1
y = x - 1 → y - x = -1 → 2y - 2x = -2
2x - 3y = -1
-2x + 2y = -2
Just add the two equation to eliminate x
2x - 3y = -1
+ -2x + 2y = -2
0x - y = -3 → y = 3
y = x - 1
3 = x - 1
x = 3+1
x = 4
x = 4, and y = 3
c.) substitution
Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1
2x - 3y = -1
if y = x-1
2x - 3(x-1) = -1
2x - 3x + 3 = -1
-x = -1 - 3
-x = -4
x = 4
y = x-1
y = 4-1
y = 3
x = 4 and y = 3
Problem
The sum of two numbers is 32 and the difference is 2. Find the numbers.
Let x is the first number and y is the other one.
x+y = 32
x-y = 2
Solve using Elimination Method
x + y = 32
x - y = 2
add the two equation to eliminate y
x+y = 32
x-y = 2
2x = 34
x = 17
x+y = 32
17+y = 32
y = 32-17
y = 15
The two numbers are 15 and 17.
