Question

Solve for $x$:

$3x+4y=85;6x+7y=20$

Answer 1

Step 1: Find value of $y$

$$\begin{gathered} 3x+4y=85...........................\left(i\right) \\ 6x+7y=20..........................\left(ii\right) \end{gathered}$$

Multiply the equation (i) with $2$

$6x+8y=170..................\left(iii\right)$

Now subtract equation (ii) from (iii)

$$\begin{gathered} \underline{6x+8y=170 \\ 6x+7y=20 \\ \left(-\right)\left(-\right)\left(-\right)} \\ 0+y=150 \end{gathered}$$

$y=150$

Step 2: Find value of $x$

Putting value of $y$ in equation (i) we get,

$\begin{array}{rcl}3x+4\times 150& =& 85\\ 3x+600& =& 85\\ 3x& =& 85-600\\ 3x& =& -515\\ x& =& \frac{-515}{3}\\ x& =& 171.66\\ & & \end{array}$

Hence, The value of $x=171.66andy=150$