Question

solve graphically:2x-y=2 3x+2y=17
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Answer 1

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

Given equation of lines are

$\rm :\longmapsto\:2x - y = 2$

and

$\rm :\longmapsto\:3x + 2y = 17$

Consider first equation

$\rm :\longmapsto\:2x - y = 2$

can be rewritten as

$\rm :\longmapsto\:y = 2x - 2$

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

$\rm :\longmapsto\:y = 2 \times 0- 2$

$\rm :\longmapsto\:y = 0- 2$

$\bf\implies \:y = - 2$

Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:y = 2 \times 1- 2$

$\rm :\longmapsto\:y = 2 - 2$

$\bf\implies \:y = 0$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 2 \\ \\ \sf 1 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 2) & (1 , 0)

➢ See the attachment graph.

Now, Consider second equation

$\rm :\longmapsto\:3x + 2y = 17$

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

$\rm :\longmapsto\:3 \times 0 + 2y = 17$

$\rm :\longmapsto\: 0 + 2y = 17$

$\rm :\longmapsto\: 2y = 17$

$\bf\implies \:y = 8.5$

Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:3 \times 1 + 2y = 17$

$\rm :\longmapsto\:3 + 2y = 17$

$\rm :\longmapsto\:2y = 17 - 3$

$\rm :\longmapsto\:2y = 14$

$\bf\implies \:y = 7$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 8.5 \\ \\ \sf 1 & \sf 7 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 8.5) & (1 , 7)

➢ See the attachment graph.

So, from graph, we conclude that

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{x = 3} \\ \\ &\sf{y = 4} \end{cases}\end{gathered}\end{gathered}$