Solve the simultaneous equation by elimination method:
3x – 4y = 10; 4x + 3y = 5

Hint: Eliminate either x or y then the equation in only one variable will remain and from that we will get one variable value and put that value of the variable in one of the equations and then that equation will resolve to one variable which can be easily solved.

Complete step-by-step answer:

3x – 4y = 10 --------- (1)
4x + 3y = 5 ---------- (2)
Now multiply equation (1) by 3 and multiply equation (2) by 4 and then add both the equations.
$\begin{align}
  & \left( 3x-4y=10 \right)\times 3 \\
 & \left( 4x+3y=5 \right)\times 4 \\
\end{align}$
After adding the equations like that we get:
$\begin{align}
  & 9x-12y=30 \\
 & \dfrac{16x+12y=20}{25x+00=50} \\
\end{align}$
After addition the expression we got is 25x = 50 which on further simplification will yield x = 2.
Now, we are substituting this value of x in equation (1).
3(2) – 4y = 10
$\Rightarrow $ 6 – 4y = 10
Rearranging the numeral terms one side and y term on the other side of equal to:
6 – 10 = 4y
$\Rightarrow $-4 = 4y
$\Rightarrow $-1 = y
Hence, the solution of the simultaneous equation is x = 2 and y = -1.

Note: You can also verify the solutions by satisfying the values of x and y that you have solved in one of the given simultaneous equations.
Like we have got x = 2 and y = -1 so by putting these values in equation (1), i.e. 3x – 4y = 10 we get,
3(2) – 4(-1) = 10
$\Rightarrow $6 + 4 = 10
$\Rightarrow $10 = 10
L.H.S =R.H.S
Hence, the solution of equations that we have solved is satisfying one of the equations. So, the values of x and y that we have solved are correct.