Question

Solve for x and y, $7x-9y-19=0$ and $4x+5y-21=0$ .

Answer 1

Hint: Use elimination method, any of the coefficients x or y is first equated and eliminated. After elimination the equations are solved to obtain the other equation. Thus, you get the value of x and y.

Complete step-by-step answer:
We have been given two linear equations, which we have to solve and get the value of x and y. The two linear equations are respectively,
$7x-9y-19=0$ ……………………………….(1)
$4x+5y-21=0$ ………………………………(2)
We can solve these linear equations by using elimination method, any of the coefficients is first equated and eliminated. After elimination, the equations are solved to obtain the other equation.
Let us consider equation (1), multiply the entire equation by 4. Now, in equation (2) multiply the entire equation by 7.
 $7x-9y-19=0$ ……………………………(1) $\times 4$
 $4x+5y-21=0$ …………………………..(2) $\times 7$
Thus, we get the new equations as
$28x-36y=76$
$28x+35y=147$
Now let us subtract both the equations,
$\begin{align}
  & \text{ }28x-36y=76 \\
 & \underline{{}^{\left( - \right)}28x\overset{\left( - \right)}{\mathop{+}}\,35y={}^{\left( - \right)}147} \\
 & \text{ 0 }-71y=-71 \\
\end{align}$
Thus, we get $\Rightarrow y=\dfrac{-71}{-71}=1$
Hence, we get the value of $y=1$.
Now let us put $y=1$ in equation (2)
$4x+5y=21$
$\Rightarrow 4x+5\times 1=21$
$\therefore 4x=21-5$
$\therefore x=\dfrac{16}{4}=4$
$\therefore $ we got the value of x and y as 4 and 1.
$\therefore x=4$ and $y=1$ is the solution of our equation.

Note: We can solve it using substitution method also, as
$7x=19+9y\Rightarrow x=\dfrac{19+9y}{4}$
Put the value of x in equation (2)
$4\left( \dfrac{19+9y}{4} \right)+5y=21$
$76+36y+35y=21\times 7$
$76+71y=147$
$y=1$