Solutions of Simultaneous Linear Equations: Graphical Method

Q. Erik wants to make lemonade for his friends. He used $4$ tablespoons of lemon juice for $6$ glasses of lemonade. Then he uses 8 tablespoons of lemon juice for $12$ glasses.
Which of the following is correct for the context given?

P. The number of tablespoons used and the number of glasses are in a proportional relationship.
Q. The number of tablespoons used and the number of glasses are not in a proportional relationship.

1. $P$ and $R$
2. $Q$ and $R$
3. $P$ and $Q$
4. $P,Q,$ and $R$

Q. A juice vendor prepares fruit juice by mixing apple juice and grape juice in the ratio of $5:3.$ The vendor takes an order to make $2\text{L}$ of fruit juice. Find the required quantity of grape juice using the graphical method.

1. $750\text{L}$
2. $750\text{mL}$
3. $1.2\text{L}$

Q. How many solutions do the given simultaneous linear equations have? Evaluate using the graphical method.
$-x-y=1;$
$x+y+3=0$

Q. Find the solution of the simultaneous linear equations using the graphical method.
$3y-2x=6$
$2x+y=2$

1. $(2,0)$
2. It has more than one solution.
3. None of the above.

Q. Choose the correct solution(s) of the given simulteneous linear equations.
$5x+2y=10y=-\frac{5}{2}x+5$

1. $(0,5)$
2. $(1,2.5)$
3. $(4,-6)$
4. They have infinitely many solutions.

Q. A dealer wanted to buy 30 tables and 50 chairs by spending $\$1,500.$ If cost of each chair is equal to cost of each table, find the cost of each chair. Evaluate using the graphical method.

1. $\$18.75$
2. $18$
3. $19.75$