Question

2x +3y=7,6x+5y=11 in substitution method​

Answer 1

2x +3y=7 .....(1)

6x+5y=11 .....(2)

We pick either of the equations and write one variable in terms of the other. Let us consider the equation (1)

2x +3y=7

2x=7-3y

$x = \frac{7 - 3y}{2} \: \: \: \: \: \: \: ...(3)$

Substitute the value of x in equation(2), we get

$6( \frac{7 - 3y}{2} ) + 5y= 11 \\ 21 - 9y + 5y= 11 \\ 21 - 4y = 11 \\ - 4y = 11 - 21 \\ - 4y = - 10 \\ y = \frac{10}{4} \\ y = \frac{5}{2}$

Now substituting the value of y in equation (3), we get

$x = \frac{7 - 3 (\frac{5}{2} )}{2} \\ x = \frac{7 - \frac{15}{2} }{2} \\ x = \frac{ \frac{14 - 15}{2} }{2} \\ x = \frac{ \frac{ - 1}{2} }{2} \\ x = \frac{ - 1}{2} \times \frac{1}{2} \\ x = \frac{ - 1}{4}$