Question

If the points $A(3,5)$ and $B(1,4)$ lie on the graph, of the line $ax+by=7$, then the sum of value of ‘$a$’ and ‘$b$’ is

• A. $4$
• B. $-1$
• C. $2$
• D. $1$

Answer 1

The correct option is D

$1$

Step 1: Determine the equation and solve it to get the value of $a\text{and}b$.

Since the point $A(3,5)$ and $B(1,4)$, pass through the equation $ax+by=7$, they satisfy the equation. Therefore, we can substitute the values to get two equations.

$3a+5b=7\cdots \mathbf{\text{(i)}}$

$a+4b=7\cdots \mathbf{\text{(ii)}}$

Solving both the equations simultaneously to get the value of :

$\Rightarrow \begin{array}{ccc}3a+5b=7& \cdots \left(\text{i}\right)& \times 1\\ a+4b=7& \cdots \left(\text{ii}\right)& \times 3\end{array}$

$$\begin{gathered} \Rightarrow 3a-3a05b=-12b=-7b=7-21-14 \\ \Rightarrow -7b=-14 \\ \Rightarrow b=2\cdots \left(\text{iii}\right) \end{gathered}$$

Therefore $b=2$, putting the value of $b$, in eq $\left(\text{ii}\right)$ to obtain the value of $a$.

$$\begin{gathered} \Rightarrow a+4\times \left(2\right)=7 \\ \Rightarrow a+8=7 \\ \Rightarrow a=7-8 \\ \Rightarrow a=-1 \end{gathered}$$

Step 2: Find the sum of ‘$a$’ and ‘$b$’ :

Thus, the sum of the value of ‘$a$’ and ‘$b$’ is

$$\begin{gathered} \Rightarrow a+b=-1+2 \\ \Rightarrow =1 \end{gathered}$$

Thus,3 the correct answer is Option D