Question

Solve the given equations.
$2x + 3y = 11$ and $2x - 4y = - 24$.

Answer 1

Hint – There can be two ways to solve two equations involving two variables, the first one is by elimination. We will be making the coefficient of any one of either x or y same in both the equations and then subtracting or adding these equations to neutralize one variable. The second method will be explained at the latter end.

Complete step-by-step answer:

Given linear equations are
$2x + 3y = 11$……………………………………. (1)
$2x - 4y = - 24$…………………………….. (2)

Now use elimination method to solve these linear equations so subtract equation (2) from equation (1) we have,
$ \Rightarrow 2x + 3y - \left( {2x - 4y} \right) = 11 - \left( { - 24} \right)$

Now simplify the above equation we have,
$ \Rightarrow 2x + 3y - 2x + 4y = 11 + 24$

Now as we see 2x is eliminated
$ \Rightarrow 7y = 35$

Now divide by 7 throughout we have,
$ \Rightarrow y = \dfrac{{35}}{7} = 5$

Now put the value of y in equation (1) we have,
$ \Rightarrow 2x + \left( {3 \times 5} \right) = 11$

Now simplify the above equation we have,
$ \Rightarrow 2x = 11 - 15 = - 4$
$ \Rightarrow x = \dfrac{{ - 4}}{2} = - 2$

So the required solution of the linear equations is (-2, 5).

So this is the required answer.

Note – The second method is substitution, in this we take out one variable in terms of another variable using a single equation and then putting this value into the second equation. This helps convert the second equation into a single variable only and thus values could be found.