91Ó°ÊÓ

In this question system of two equations $$\begin{gathered} \left\{4x+2y=2 \\ -4x−3y=−9\right\} \end{gathered}$$are given.

We need to find the solution to these equations

In the question, both equations are in standard form, and to eliminate we need to add both equations since coe. x is the opposite. Then,

$$\begin{gathered} 4\mathrm{x}+2\mathrm{y}=2\left(1\right) \\ -4\mathrm{x}-3\mathrm{y}=-9\left(2\right) \\ \mathrm{when}\left(1\right)+\left(2\right)⇒-\mathrm{y}=-7 \\ \mathrm{y}=7 \\ \mathrm{to}\mathrm{get}\mathrm{value}\mathrm{for}\mathrm{the}\mathrm{variable}\mathrm{x}\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{sustitute}\mathrm{y}=7\mathrm{in}\left(1\right)\mathrm{or}\left(2\right) \\ \mathrm{then}\mathrm{put}\mathrm{y}=7\mathrm{in}\left(1\right)\mathrm{we}\mathrm{get}4\mathrm{x}+2×7=2 \\ 4\mathrm{x}=2-14 \\ \mathrm{x}=-\frac{12}{4} \\ =-3 \\ \mathrm{now}\mathrm{the}\mathrm{solution}\mathrm{for}\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{are}(-3,7) \end{gathered}$$

To check the original solution, we have to substitute solution (-3,7) in the given system equations and if both sides are equal in the given equations then (-3,7) is the original solution. Then

$$\begin{gathered} 4\mathrm{x}+2\mathrm{y}=2,\mathrm{put}\mathrm{x}=-3,\mathrm{y}=7\mathrm{in}\mathrm{this}\mathrm{orginal}\mathrm{equation}\mathrm{we}\mathrm{get} \\ -3×4+2×7=2 \\ -12+14=2 \\ 2=2,\mathrm{both}\mathrm{sides}\mathrm{are}\mathrm{equal} \\ -4\mathrm{x}-3\mathrm{y}=-9.\mathrm{substitue}\mathrm{the}\mathrm{values}\mathrm{x}=-3\mathrm{and}\mathrm{y}=7\mathrm{then} \\ -4×-3-3×7=-9 \\ 12-21\mathrm{c}=-9 \\ -9=-9,\mathrm{both}\mathrm{sides}\mathrm{are}\mathrm{equal} \\ \mathrm{So}\mathrm{ordered}\mathrm{pair}(-3,7)\mathrm{is}\mathrm{a}\mathrm{solution}\mathrm{for}\mathrm{given}\mathrm{equations} \end{gathered}$$