Question

The following equations are an example of a consistent pair of equations.
3x+2y=5 ; 2x−3y=7
A. True
B. False

Answer 1

Hint: In this particular type of question we need to solve both equations and check whether the system is consistent or inconsistent. To solve both the equations we need to multiply both of them with a constant and subtract to eliminate one variable then substitute any equation to get the value of the eliminated variable.

Complete step-by-step answer:
Let, 3x+2y=5 $\to$ (1)

2x−3y=7 $\to$ (2)

Multiply equation (1) by 2 and equation (2) by 3

We get,

6x+4y=10 $\to$ (3)

and 6x−9y=21 $\to$ (4)

Subtract equations (3) and (4), we get

$
6x + 4y - 6x + 9y = 10 - 21 \\

\Rightarrow 13y = - 11 \\

\Rightarrow y = \dfrac{{ - 11}}{{13}} \\

$

Substitute the value of y in (1) , we get

$3x + 2\left( { - \dfrac{{11}}{3}} \right) = 5$

$

\Rightarrow 3x - \dfrac{{22}}{{13}} = 5 \\

\Rightarrow 3x = \dfrac{{87}}{3} \\

\Rightarrow x = \dfrac{{29}}{{13}} \\

$

$\therefore x = \dfrac{{29}}{{13}},y = \dfrac{{ - 11}}{{13}}$

Hence, the pair of equations are consistent.

The correct answer is A.

Note: Remember that in mathematics and particularly in algebra, a linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In short if both equations have a common solution or the lines meet at some point then the lines are consistent.