Question

Draw a graph for each pair of equations and find their solution a) 5x + 2y =20
y = 2x + 1

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equations are

$\rm \: 5x + 2y = 20$

and

$\rm \: y = 2x + 1$

Consider

$\rm \: 5x + 2y = 20$

Substituting 'x = 0' in the given equation, we get

$\rm \: 5(0) + 2y = 20$

$\rm \: 0 + 2y = 20$

$\rm \: 2y = 20$

$\rm\implies \:y = 10$

Substituting 'y = 0' in the given equation, we get

$\rm \: 5x + 2(0) = 20$

$\rm \: 5x + 0 = 20$

$\rm \: 5x = 20$

$\rm\implies \:x = 4$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 10 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

Now, Consider

$\rm \: y = 2x + 1$

Substituting 'x = 0' in the given equation, we get

$\rm \: y = 2(0) + 1$

$\rm \: y = 0 + 1$

$\rm\implies \:y = 1$

Substituting 'y = 0' in the given equation, we get

$\rm \: 0 = 2x + 1$

$\rm \: 2x = - 1$

$\rm\implies \:x = - 0.5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 1 \\ \\ \sf - 0.5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the graph in attachment.

So, from graph, we concluded that, solution of equations is given by

$\begin{gathered}\begin{gathered}\bf\: \begin{cases} &\sf{x = 2} \\ \\ &\sf{y = 5} \end{cases}\end{gathered}\end{gathered}$