Question

Solve the following linear equation by substitution method:
8x - 3y = 12, 5x = 2y + 7

Answer 1

Hint – In this question take any one equation say $8x - 3y = 12$, and find one variable in terms of another variable, then use this relation to substitute the value of this variable into the second equation which is $5x - 2y = 7$.
Complete step-by-step answer:
Given equations
$8x - 3y = 12,{\text{ 5}}x = 2y + 7$
$8x - 3y = 12$………………… (1)
$5x - 2y = 7$…………………………. (2)
Now use Substitution method to solve these equations
So, from equation (1) calculate the value of y we have,
$ \Rightarrow 3y = 8x - 12$
Now divide by 3 we have,
$ \Rightarrow y = \dfrac{{8x - 12}}{3}$
Now put this value of y in equation (2) we have,
$ \Rightarrow 5x - 2\left( {\dfrac{{8x - 12}}{3}} \right) = 7$
Now simplify the above equation we have,
$ \Rightarrow 15x - 16x + 24 = 21$
$ \Rightarrow - x = 21 - 24 = - 3$
$ \Rightarrow x = 3$
Now substitute the value of x in equation (1) we have,
$ \Rightarrow 8 \times 3 - 3y = 12$
Now simplify the above equation we have,
$ \Rightarrow 3y = 24 - 12 = 12$
$ \Rightarrow y = \dfrac{{12}}{3} = 4$
So, x = 3 and y = 4 is the required solution of the equation.

Note – Since it is specifically asked to solve with a method of substitution hence we have used it otherwise, there is another method to solve problems of this kind. This method is the method of elimination, in which we make coefficients of any one variable in both the equations the same and then eliminate them by performing addition/subtraction.