Page 34 - Algebra 1

Simultaneous Equation
A linear equation in two variables is given by px + qy + r = 0, where p ≠ 0, q ≠ 0
When we have two linear equations in two variables, they are called simultaneous equation. p1x + q1y + r1 = 0
p2x + q2y + r2 = 0
p1, p2, q1, q2, r1, r2 are all real numbers.
You can find the solution to these two equations either by elimination or substitution.
REMEMBER:
p1x + q1y + r1 = 0
p2x + q2y + r2 = 0
If these two are simultaneous equations, then
𝑝1 𝑞1
12. 𝑝2 ≠ 𝑞2, then the pair of linear equation has a unique solution.
𝑝1 𝑞1 𝑟1
13. 𝑝2 = 𝑞2 ≠ 𝑟2, then the pair of linear equation has no solution.
𝑝1 𝑞1 𝑟1
14. 𝑝2 = 𝑞2 = 𝑟2,, then the pair of linear equation has infinite solutions.
Worked Example 13
Find the solution of the following pair of equations.
3+y=3 𝑥
5 + 2y = 5 𝑥
Solution:
Let1 =p 𝑥
Then, the system of equation is 3p + y – 3 = 0 .............................. (1) 5p + 2y – 5 = 0 ............................ (2)
Multiply (1) by 2
6p + 2y – 6 = 0 .............................. (3) (3) – (2)
6p + 2y – 6 = 0
– 5p – 2y + 5 = 0 p–1=0
p=1
1=p 𝑥
x=1
Substitute x =1 in the first equation.
3+y=3 𝑥
3+y=3 1
y=0
The solution of the pair of linear equation is (1, 0).
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ALGEBRA