Solutions of Simultaneous Linear Equations: Elimination Method

Q. If $2$ is added to the numerator and denominator of a fraction, it becomes $9/10.$ If $3$ is subtracted from the numerator and denominator of the same fraction, it becomes $4/5.$ What is the fraction?

1. $\frac{5}{6}$
2. $\frac{6}{7}$
3. $\frac{7}{8}$
4. $\frac{8}{9}$

Q. Solve the simultaneous equations using elimination method.
$7x+2y=12$
$2x-17y=25$

1. $(\frac{109}{51},-\frac{151}{102})$
2. $(-\frac{151}{102},\frac{109}{51})$

Q.

How do you solve a system of equations by using the elimination method?

Q. The solution of the pair of linear equations $2y+7x=-5$ and $5y-7x=12$ is

1. $(1,1)$
2. $(1,-1)$
3. $(-1,-1)$
4. $(-1,1)$

Q. Solutions of the pair of equations $2x+5y=3$ and $3x-2y=1$
using elimination method is

1. $(\frac{11}{19},\frac{7}{19})$
2. $(\frac{11}{19},\frac{3}{19})$
3. $(\frac{7}{19},\frac{3}{19})$
4. $(-\frac{11}{19},\frac{7}{19})$

Q. The lines plotted on the attached graph have a solution$(2,5)$

1. True
2. False

Q. After five years, the age of son will be half the age of his father's present age. Five years ago, sum of their age was 75 years.

The present age of the father is years.

The present age of the son is years.

Solve using elimination method.

Q. Find the solution for the following pair of equations
$4x+5y=-4$
$3x-2y=-3$

1. $(1,3)$
2. $(-1,0)$
3. $(2,\frac{9}{2})$
4. $(0,0)$

Q. Find the solution for the following pair of equations
$2x+y=8$
$3x-2y=5$

1. $(2,4)$
2. $(3,2)$
3. $(1,-1)$
4. $(-1,10)$

Q. Find the solution for the following pair of equations
$2x+y=3$
$3x-y=7$

1. $(1,1)$
2. $(3,2)$
3. $(2,-1)$
4. $(-1,4)$

Q.

Solve the following system of equations

$\frac{4}{x}+5y=7;\frac{3}{x}+4y=5$

Q. Sum of the digits of a two digit number is 5 and difference of the digits is 1. Also, the tens place is greater than the unit place digit. The number is .

Q. Consider the following statements:

Statements I: When two simultaneous equations are added or subtracted, the resulting solution does not change.

Statements II: When one of the two simultaneous equations is multiplied with a constant and added with the other equation, the resulting solution does not remain same.

Choose the correct option based on the statements.

1. Both the statements are correct.
2. Only statement I is correct.

Q. Find the solution for the following pair of equations
$2x+8y=3$
$2x+y=\frac{5}{4}$

1. $(1,-\frac{3}{4})$
2. $(1,\frac{1}{4})$
3. $(\frac{1}{4},\frac{5}{16})$
4. $(\frac{1}{2},\frac{1}{4})$

Q. Which of the following is the solution for the given system of two linear equations $x+y=2$ and $2x-y=3?$

1. $(\frac{5}{3},\frac{1}{3})$
2. $(\frac{1}{3},\frac{5}{3})$
3. $(\frac{5}{3},\frac{-1}{3})$
4. $(\frac{-5}{3},\frac{1}{3})$

Q. $2$ men and $6$ boys can do work equivalent to $15$ days. With similar efficiency, $1$ man and $4$ boys can do another work equivalent to $12$ days.
Are these statements correct?

1. Yes. There exist a solution.
2. No. There is no feasible solution.