Question

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Answer 1

Question 1:-

The following pairs of linear equations are consistent or inconsistent. If consistent solve it by graphical method.

1. $\begin{cases} & x+y=5 \\ & 2x-3y=4 \end{cases}$
2. $\begin{cases} & 3x+4y=10 \\ & 2x-2y=2 \end{cases}$

The solution to Question 1:-

Both pairs are inconsistent as $\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}$.

Each pair of line colored in red or green intersect each other at $(\dfrac{19}{5} ,\dfrac{6}{5} )$ or $(2,1)$.

Question 2:-

Solve $\begin{cases} & x+3y=6 \\ & 2x-3y=12 \end{cases}$ graphically.

The solution to Question 2:-

The pair of lines intersect each other at $(6,0)$. Hence $x=6$ and $y=0$.

Question 3:-

The coach of a cricket team buys,

• 7 bats and 6 balls for 3800.
• 3 bats and 5 balls for 1750.

The solution to Question 3:-

Assign variables $x,y$ to the cost of each bat and ball.

• Bats: $x$
• Balls: $y$

$\begin{cases} & 7x+6y=3800 \\ & 3x+5y=1750 \end{cases}$

The pair of lines intersect each other at $(500,50)$. The cost of each bat and ball are $500$ and $50$ respectively.

Refer to the attachment for graphical method.