Question

graph the system of equations given below on the provided graph 2x - 3y = - 18
3x + y = -5

Answer 1

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

Consider first equation

$\rm \: 2x - 3y = - 18$

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

$\rm \: 2 \times 0 - 3y = - 18$

$\rm \: 0 - 3y = - 18$

$\rm \: - 3y = - 18$

$\rm\implies \:y = 6$

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

$\rm \: 2x - 3 \times 0 = - 18$

$\rm \: 2x - 0 = - 18$

$\rm \: 2x= - 18$

$\rm\implies \:x = \: - \: 9$

Hᴇɴᴄᴇ,

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

$\green{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf - 9 & \sf 0 \end{array}} \\ \end{gathered}}$

Consider second equation

$\rm \: 3x + y = - 5$

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

$\rm \: 3 \times 0 + y = - 5$

$\rm \: 0 + y = - 5$

$\rm\implies \:y = \: - \: 5$

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

$\rm \: 3 \times ( - 1) + y = - 5$

$\rm \: - 3 + y = - 5$

$\rm \: y = - 5 + 3$

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

Hᴇɴᴄᴇ,

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

$\purple{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 5 \\ \\ \sf - 1 & \sf - 2 \end{array}} \\ \end{gathered}}$

➢ Now draw a graph using the points (0 , 6), (- 9, 0), (0, - 5) & (- 1 , - 2)

➢ See the attachment graph.

Hence, from graph we concluded that given system of equations is consistent having unique solution and solution is

$\red{\rm\implies \:\boxed{ \rm{ \: \: x \: = \: - \: 3 \: }} \: \: and \: \: \boxed{ \rm{ \:y \: = \: 4 \: \: }} }$