Question 1 :
Solve the equations using elimination method:<br>$$2x - y = 20$$ and $$4x + 3y = 0$$
Question 2 :
Find the value of $$x$$ and $$y$$ using cross multiplication method: <br/>$$3x + 5y = 17$$ and $$2x + y = 9$$
Question 3 :
Determine the values of a and b for which the following system of linear equation has infinite solutions.<br>$$2x-(a-4)y=2b+1$$<br>$$4x-(a-1)y=5b-1$$<br>
Question 4 :
Let the equation $$x + y +z = 5, x + 2y + 2z = 6, x + 3y + \lambda z = \mu$$ have infinite solution then the value of $$\lambda \mu $$ is$$10$$
Question 5 :
The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are respectively,
Question 6 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:$$1.5x + 0.1y = 6.2$$, $$3x - 0.4y = 11.2$$
Question 7 :
If $$2p + 3q = 18$$ and $$4p^{2} + 4pq - 3q^{2} - 36 = 0$$ then what is $$(2p + q)$$ equal to?
Question 8 :
Find the values of $$x$$ and $$y$$, if $$\displaystyle \frac{2}{x}\, +\, \frac{6}{y}\, =\, 13;\quad \frac{3}{x}\, +\, \frac{4}{y}\, =\, 12$$
Question 9 :
Solve : $$\displaystyle \frac{9}{x}\, -\, \displaystyle \frac{4}{y}\, =\, 8$$ and $$\displaystyle \frac{13}{x}\, +\, \displaystyle \frac{7}{y}\, =\, 101$$
Question 10 :
Solve the equations using cross multiplication method: $$3x + 2y = 10$$ and $$4x - 2y = 4$$<br/>
Question 11 :
Is the following situation possible? If so, determine their present ages.<br>The sum of the ages of two friends is $$20$$ years.Four years ago, the product of their ages in years was $$48$$.
Question 12 :
Solve the following pair of simultaneous equations:$$8a\, -\, 7b\, =\, 1$$<br/>$$4a\, =\, 3b\, +\, 5$$
Question 13 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$$0.2x+0.1y= 25$$<br/>$$2\left ( x-2 \right )-1.6y= 116$$
Question 15 :
Solve : $$\displaystyle \frac{3}{x+y}+\displaystyle \frac{2}{x-y}= 2$$ and $$\displaystyle \frac{9}{x+y}-\displaystyle \frac{4}{x-y}= 1$$
Question 16 :
If $$(3)^{x + y} = 81$$ and $$(81)^{x - y} = 3$$, then the values of $$x$$ and $$y$$ are<br>
Question 17 :
Solve: $$\displaystyle \frac{3}{x}-\displaystyle \frac{2}{y}= 0$$ and $$\displaystyle \frac{2}{x}+\displaystyle \frac{5}{y}= 19$$. Hence, find $$a$$ if $$y= ax+3$$.
Question 18 :
Solve the equations using elimination method:<br>$$2x + 3y = 12$$ and $$4x + 2y = 8$$
Question 20 :
Solve the following pair of equations:<br/>$$41x + 53y = 135$$, $$53x + 41y = 147$$
Question 21 :
Find the value of x and y using cross multiplication method:<br/>$$ x + 2y = 8$$ and $$2x -3y = 2$$
Question 22 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$$\dfrac {10}{(x+y)}+\dfrac {2}{(x-y)}=4, \dfrac {15}{(x+y)}-\dfrac {5}{(x-y)}=-2$$<br/>
Question 23 :
Solve the following pairs of linear equations by elimination method:<br/>$$217x + 131y = 913$$ and $$131x + 217y = 827$$<br/>
Question 24 :
Find the value of x and y using cross multiplication method: <br>$$5x + 2y = 32$$ and $$6x + 6y = 42$$
