Pair of Linear Equations in Two Variables

On comparing the ratios $\frac{a_1}{a_2}, \frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

On comparing the ratios $\frac{a_1}{a_2}, \frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pair of linear equations are consistent, or inconsistent.

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Given the linear equation $2x + 3y - 8 = 0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

Solve the following pair of linear equations by the substitution method.

Solve $2x + 3y = 11$ and $2x - 4y = -24$ and hence find the value of ‘$m$’ for which $y = mx + 3$.

Form the pair of linear equations for the following problems and find their solution by substitution method.

Solve the following pair of linear equations by the elimination method and the substitution method:

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: