Simultaneous Equations

The sum of father's age and twice the age of his son is $70 .$ If we double the age of the father and add it to the age of his son the sum is $95 .$ Find the present age of the father.

Solve:
$x+y=6$
$x-y=2$

If $x+y=5$ and $x-y=1$, then find the value of $x$.

Two types of boxes $A, B$ are to be placed in a truck having capacity of $10$ tons. When $150$ boxes of type $A$ and $100$ boxes of type$B$ are loaded in the truck, it weighs $10$ tons. But when $260$ boxes of type $A$ are loaded in the truck, it can still accommodate $40$ boxes of type $B$, so that it is fully loaded. Find the weight of each type of box.

The sum of father's age and twice the age of his son is $70 .$ If we double the age of the father and add it to the age of his son the sum is $95 .$ Find their present ages.

Complete the following.

Two numbers differ by $3$. The sum of twice the smaller number and thrice the greater number is $19 .$ Find the numbers.

Solve the following simultaneous equations.

$49 x-57 y=172 ; 57 x-49 y=252$

Solve the following simultaneous equations.

$99 x+101 y=499 ; 101 x+99 y=501$

Solve the following simultaneous equations.

$\frac{1}{3}x+y=\frac{10}{3};2x+\frac{1}{4}y=\frac{11}{4}$

Solve the following simultaneous equations.

$5 x+2 y=-3 ; x+5 y=4$

Solve the following simultaneous equations.

$5 m-3 n=19 ; m-6 n=-7$

Solve the following simultaneous equations.

$x+7 y=10 ; 3 x-2 y=7$

Solve the following simultaneous equations.

$3 a+5 b=26 ; a+5 b=22$

In a factory the ratio of the salary of skilled and unskilled workers is $5:3$. The total salary of one day of both of them is $₹720$. Find daily wages of skilled and unskilled workers.

Kantabai bought $1\frac{1}{2} \mathrm{kg}$ tea and $5 \mathrm{kg}$ sugar from a shop. She paid $₹50$ as return fare for rickshaw. Total expense was $₹700$. Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for $2 \mathrm{kg}$ tea and $7 \mathrm{kg}$ sugar. She paid $₹ 880$ for that. Find the rate of sugar and tea per $\mathrm{kg}$.

Solve the following word problems.

A two-digit number and the number with digits interchanged add up to $143$. In the given number the digit in the unit's place is $3$ more than the digit in the ten's place. Find the original number.

Solve the following simultaneous equations.

$\frac{7x-2y}{xy}=5; \frac{8x+7y}{xy}=15$

Solve the following simultaneous equations.

$\frac{7}{2x+1}+\frac{13}{y+2}=27; \frac{13}{2x+1}+\frac{7}{y+2}=33$

Anushka got $₹2500$ from Anand in the denomination of $₹100$ and $₹50$. If Anand would have given her the amount by interchanging the number of notes, Anushka would have received $₹500$ less than the previous amount. Find the number of notes that Anushka had.