Question

Solve $x-2y=0,3x+4y=20$.

Answer 1

The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree $1$ (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable.

$ax+b=0$, where, $a\ne 0$ and $x$ is the variable.

Given:

$x-2y=0$………$1$

$3x+4y=20$……..$2$

Multiplying the Equation $1$ by $2$ we get:

$2x-4y=0$……..eq$3$

Adding equations $2$ and $3$ we get,

$$\begin{gathered} 3x+4y+2x-4y=20+0 \\ \Rightarrow 5x=20 \\ \Rightarrow x=\frac{20}{5} \\ \Rightarrow x=4 \end{gathered}$$

Substituting the value of $x$ in equation $1$ we get,

$$\begin{gathered} \Rightarrow 4-2y=0 \\ \Rightarrow 4=2y \\ \Rightarrow y=\frac{4}{2} \\ \Rightarrow y=2 \end{gathered}$$

Hence $x=5$ and $y=2$