Math activity

Pair of linear equations in two variables

Geometric [graphical] solution

Algebraic solution

Single and unique solution

No solutions at all

Inconsistent

Parallel lines

Intersecting lines

Identical and overlapping lines

Infinitely many solutions

Consistent

Consistent

If the Pair of linear equations are ax+by+c=0 and Ax+By+C=0 then a/A≠b/B≠c/C

If the Pair of linear equations are ax+by+c=0 and Ax+By+C=0 then a/A=b/B=c/C

If the Pair of linear equations are ax+by+c=0 and Ax+By+C=0 then a/A=b/B≠c/C

In Pair of equations with variables in the Denominator we change the Fraction To another variable

We take (1/x) as 'p' and (1/y) as 'q'

After solving for 'p' and 'q' we solve for (1/x)=p and (1/y)=q

Then the Equations are 2p+3q=13 and 5p-4q=-2

Eg. Let the Pair of Equations be 2/x+3/y= 13 and 5/x-4/y=-2

We substitute the value of one variable by Expressing it in the Term of the other variable to solve the Pair of linear equations

Equations Reducible to a pair of linear equations

Substitution method

Elimination method

Cross Multiplication Method

We eliminate one variable first to get a linear equation in one variable and then solving it we find the other variable

If the Pair of linear equations are ax+by+c=0 and Ax+By+C=0 then x/(b*-B*c)=y/(c*A-C*a)=1/(a*B-A*b)