Question

Identify the correct answer which satisfies the linear equations: $3x+7y=14$ and $2x+7y=21$

• A. $(-7,5)$
• B. $(7,5)$
• C. $(7,-5)$
• D. $(-7,-5)$

Answer 1

The correct option is A $(-7,5)$

$3x+7y=14$ ----- (1)
$2x+7y=21$ ----- (2)
Substitute the values of first option $x=-7$ and $y=5$ in equations 1 and 2
$3(-7)+7\left(5\right)=14$
$-21+35=14$
$14=14$
$2(-7)+7\left(5\right)=21$
$-14+35=21$
$21=21$
Therefore, the first option satisfied the linear equations.
Likewise substitute the value of second option $x=7,y=5$
$3\left(7\right)+7\left(5\right)=14$
$21+35=14$
$56\ne 14$
$2\left(7\right)+7\left(5\right)=21$
$14+35=21$
$49\ne 21$
Similarly, check the options to satisfy the linear equation.
Here, the first option satisfied the linear equation.
The solution is $(-7,5)$