Solve the equations: 2 x+y=6 and 4 x+2 y=5.

Question

Solve the equations: $2 x+y=6$ and $4 x+2 y=5$.

✓

Answer

$
\begin{array}{c}
2 x+y=6 \\
\therefore 2 x+y-6=0
\end{array}
$
Comparing with
$
a_1 x+b_1 y+c_1=0,
$
we have
$
a_1=2, b_1=1, c_1=-6
$
$
\begin{array}{c}
4 x+2 y=5 \\
\therefore \quad 4 x+2 y-5=0
\end{array}
$
Comparing with
$
a_2 x+b_2 y+c_2=0,
$
we have
$
a_2=4, b_2=2, c_2=-5
$
$
\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}, \frac{b_1}{b_2}=\frac{1}{2}, \frac{c_1}{c_2}=\frac{-6}{-5}=\frac{6}{5}
$
Here, $\frac{a_1}{a_2}=\frac{b_1}{b_2}$ but $\frac{a_1}{a_2} \neq \frac{c_1}{c_2}$ and $\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
$\therefore$ Solution set of the given equations is $\phi$.

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