Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:
$2x - 3y = 7$, $5x + y = 9$
(a) x = 2 and y = - 1
(b) x = 4 and y = 0
(c) x = - 3 and y = - 5
(d) x = - 7 and y = 6

Answer 1

Hint – In this question directly consider one of the two given equations and find one variable in terms of another variable. Use this relation in the other equation to form that equation into an equation of a single variable only, solve it to find that variable, then use this obtained value to get the other variable.

Complete step-by-step answer:
Given equations:
$2x - 3y = 7$.................. (1)
$5x + y = 9$................... (2)
Now we have to solve these linear equations by the method of elimination by substitution.
So from equation (1) calculate the value of x in terms of y we have,
$ \Rightarrow 2x = 3y + 7$
$ \Rightarrow x = \dfrac{{3y + 7}}{2}$.................. (3)
Now substitute this value in equation (2) we have,
$ \Rightarrow 5\left( {\dfrac{{3y + 7}}{2}} \right) + y = 9$
Now simplify this equation by multiplying 2 throughout we have,
$ \Rightarrow 5\left( {3y + 7} \right) + 2y = 18$
$ \Rightarrow 15y + 35 + 2y = 18$
$ \Rightarrow 17y = 18 - 35 = - 17$
$ \Rightarrow y = \dfrac{{ - 17}}{{17}} = - 1$
Now substitute this value in equation (3) we have,
$ \Rightarrow x = \dfrac{{3\left( { - 1} \right) + 7}}{2} = \dfrac{{ - 3 + 7}}{2} = \dfrac{4}{2} = 2$
So the required solution of the pairs of linear (simultaneous) equation by the method of elimination by substitution is (x, y) = (2, -1)
So this is the required answer.
Hence option (A) is the correct answer.

Note – This question is specifically asked by substitution but there can be another way to solve linear equations involving two variables that is the method of elimination. In this we make the coefficients of any one variable in both the equations equal and then eliminate this variable by simple operation of addition/subtraction. Then we are left with the non-eliminated variable, solve it and then use another equation to get the initially eliminated variable.