Question

Solve for x and y:
$$\begin{gathered} 2x-y+3=0 \\ 3x-7y+10=0 \end{gathered}$$

Answer 1

The given system of equations is
$$\begin{gathered} 2x-y+3=0.....\left(i\right) \\ 3x-7y+10=0.....\left(ii\right) \end{gathered}$$
From (i), write y in terms of x to get
y = 2x + 3
Substituting y = 2x + 3 in (ii), we get
$$\begin{gathered} 3x-7\left(2x+3\right)+10=0 \\ \Rightarrow 3x-14x-21+10=0 \\ \Rightarrow -7x=21-10=11 \\ \Rightarrow x=-\frac{11}{7} \end{gathered}$$
Now, substituting $x=-\frac{11}{7}$ in (i), we have
$$\begin{gathered} -\frac{22}{7}-y+3=0 \\ \Rightarrow y=3-\frac{22}{7}=-\frac{1}{7} \end{gathered}$$
Hence, $x=-\frac{11}{7}$ and $y=-\frac{1}{7}$.