Question

The solution of equations $x+y=10$, $2x+y=18$ and $4x-3y=26$ will be

• A. only one solution
• B. no solution
• C. infinite solution
• D. none of these

Answer 1

The correct option is A

only one solution

Explanation for the correct option

Given: $x+y=10----\left(1\right)$

$2x+y=18-----\left(2\right)$

$4x-3y=26-----\left(3\right)$

Subtracting both sides equation $\left(1\right)$ and $\left(2\right)$

$$\begin{gathered} \Rightarrow -x=-8 \\ \Rightarrow x=8 \end{gathered}$$

Put the value of $x$ in equation $\left(1\right)$

$$\begin{gathered} \Rightarrow 8+y=10 \\ \Rightarrow y=2 \end{gathered}$$

Similarly, Multiply equation $\left(2\right)$ by $2$

$$\begin{gathered} \left(2x+y\right)\times 2=18\times 2-----\left(2\right) \\ 4x+2y=36 \\ 4x-3y=26-----\left(3\right) \end{gathered}$$

Subtracting both sides

$$\begin{gathered} \Rightarrow 5y=10 \\ \Rightarrow y=2 \end{gathered}$$

Put the value of $y$ in the equation $\left(2\right)$

$$\begin{gathered} \Rightarrow 2x+2=18 \\ \Rightarrow 2x=16 \\ \Rightarrow x=8 \end{gathered}$$

$$\begin{gathered} \left(x+y\right)\times 3=10\times 3----\left(1\right) \\ 3x-3y=30 \\ 4x-3y=26----\left(3\right) \end{gathered}$$

Add both sides

$$\begin{gathered} \Rightarrow 7x=56 \\ \Rightarrow x=8 \end{gathered}$$

Put the value of $x$ in the equation $\left(1\right)$

$$\begin{gathered} \Rightarrow 8+y=10 \\ \Rightarrow y=2 \end{gathered}$$

Therefore $x+y=10$, $2x+y=18$ and $4x-3y=26$ has only one solution $(8,2)$

Hence, option (A) is correct.