Question

Choose the correct answer which satisfies the linear equations: $2a+5b=13$ and $a+6b=10$

• A. $(4,-1)$
• B. $(4,1)$
• C. $(-4,-1)$
• D. $(-4,1)$

Answer 1

The correct option is B $(4,1)$

$2a+5b=13$ ----- (1)
$a+6b=10$ ----- (2)
Substitute the values of first option $a=4$ and $b=-1$ in equations 1 and 2
$2a+5b=13$
$2\left(4\right)+5(-1)=13$
$85=13$
$3\ne 13$
$a+6b=10$
$4+6(-1)=10$
$46=10$
$-2\ne 10$
Therefore, the first option not satisfied the linear equations.
Likewise substitute the value of second option $a=4,b=1$
$a+5b=13$
$2\left(4\right)+5\left(1\right)=13$
$8+5=13$
$13=13$
$a+6b=10$
$4+6\left(1\right)=10$
$4+6=10$
$10=10$
Similarly, check the options to satisfy the linear equation.
Here, the second option satisfied the linear equation.
The solution is $(4,1)$