CBSE Questions for Class 12 Commerce Applied Mathematics Linear Equations Quiz 1 - MCQExams.com

Solve the following equations by substitution method.
$$2x-3y=14; \, \, 5x+2y=16$$
  • $$x = 7, y= 1$$
  • $$x = 4, y= -2$$
  • $$x = 6, y= -2$$
  • $$x = 3, y= -1$$
IF $$x - 2y = -1$$, $$y=-\dfrac { 1 }{ 2 } $$, then find the value of $$x$$ 
  • $$-2$$
  • $$-1$$
  • $$0$$
  • $$2$$
Giri is 20 year older than his son. If the sum of their ages ishow old is his son?
  • 5 years
  • 20 years
  • 25 years
  • 30 years
If $$\cfrac { a }{ x+y } =\cfrac { b }{ y+z } =\cfrac { c }{ z-x } $$, then which of the following equations is true?
  • $$a=b+c$$
  • $$c=a+b$$
  • $$b=a\times c$$
  • $$b=a+c$$
Given that $$3x-y=-11$$ and $$4x+y=4$$. Calculate the value of $$x$$.
  • $$-7$$
  • $$-1$$
  • $$8$$
  • $$15$$
The cost of 9 chairs and 3 tables is Rs. 306, while the cost of 6 chairs and 3 tables is Rs.Then the cost of 6 chairs and 1 table is
  • Rs. 161
  • Rs. 162
  • Rs. 169
  • Rs. 175
If, $$\displaystyle \frac{1}{x}+\frac{1}{y}=k$$ and $$\displaystyle \frac{1}{x}-\frac{1}{y}=k$$, then the value of y .................
  • $$3$$
  • $$-4$$
  • Does not exist.
  • None of these
Given that $$4x-3y=6$$ and $$x-3y=-3$$, the value of $$y$$ is
  • $$-3$$
  • $$-2$$
  • $$\dfrac { 4 }{ 3 } $$
  • $$2$$
The sum of two numbers is equal to $$20$$ and their difference is $$2.5$$. Find the ratio of the numbers
  • $$9 : 7$$
  • $$7 : 9$$
  • $$3 : 5$$
  • $$2 : 7$$
Solve the following pair of simultaneous equations:
$$a\, =\, b\, +\, 2$$
$$2a\, -\, b\, =\, 7$$
  • $$a = -2, b = 9$$
  • $$a = 12, b = 6$$
  • $$a = -3, b = 7$$
  • $$a = 5, b = 3$$
Given that $$2y=-6$$ and $$x-3y=13$$, the value of $$x=$$________
  • $$\dfrac { 13 }{ 9 } $$
  • $$4$$
  • $$19$$
  • $$22$$
The ratio of income of two persons is $$9 : 7$$ and the ratio of their expenditure is $$4 : 3$$.   If each of them manages to save Rs. $$2000$$ per month, find their monthly income. 
  • $$Rs. 18,000 , Rs. 14,000$$ 
  • $$Rs. 1,000 , Rs. 14,000$$ 
  • $$Rs. 18,000 , Rs. 1,000$$ 
  • None of these
If $$(a+b,1)=(5,a-b)$$, then the value of $$2a+3b=$$?
  • $$5$$
  • $$12$$
  • $$8$$
  • $$6$$
If $$\bar{x}-Z=3,$$ $$\bar{x}+Z =45$$ and $$2\bar{x}+Z=3M$$ then find $$M$$.
  • $$26$$
  • $$22$$
  • $$24$$
  • $$23$$
Solve the following system of equations by elimination method. 
$$8x-3y=5xy, 6x-5y=-2xy,x\not=0,y\not=0$$
  • $$\left ( \dfrac{11}{23}, \dfrac{22}{31} \right )$$
  • $$\left ( \dfrac{1}{23}, \dfrac{22}{31} \right )$$
  • $$\left ( \dfrac{11}{23}, \dfrac{2}{31} \right )$$
  • None of these
Solve the following system of equations by elimination method. 

$$\dfrac{3}{x}+\dfrac{5}{y}=\dfrac{20}{xy}, \dfrac{2}{x}+\dfrac{5}{y}=\dfrac{15}{xy}, x\neq 0, y\neq 0$$
  • $$(1, 5)$$
  • $$(2, 5)$$
  • $$(1, 2)$$
  • None of these
To eliminate x from equations $$x + y + 3x = 12 \rightarrow$$ ....... (1) & $$8x + 3y = 17  \rightarrow $$ ..... (2), equation (2) is to be multiplied by ..............( from the given options)
  • 8
  • $$- \dfrac{1}{2}$$
  • 3
  • None of the above
Solve the following system of equations using elimination method.
$$3x+4y=24, 20x-11y=47$$
  • $$(4 , 3)$$ 
  • $$(2 , 3)$$ 
  • $$(4 , 2)$$ 
  • None of these
The solution of $$8x+5y=9$$, $$3x+2y=4$$ lie on $$x+y=k$$, then $$k=$$
  • $$3$$
  • $$4$$
  • $$5$$
  • $$2$$
The solution of $$\sqrt{2}x+\sqrt{3}y=0$$ and $$\sqrt{3}x+\sqrt{8}y=0$$ is
  • $$(1, 2)$$
  • $$(\sqrt{2}, \sqrt{8})$$
  • $$(0, 0)$$
  • $$(\sqrt{3}, \sqrt{2})$$
If $$7$$ pens and $$3$$ books cost $$Rs 1395$$, while $$5$$ pens and $$4$$ books cost $$Rs 1665$$. Find the cost of a  book
  • $$360$$
  • $$45360$$
  • $$35350$$
  • $$none\ of\ these$$
The sum of two numbers is $$2$$ and their difference is $$1$$. Find the numbers.
  • $$2,0$$
  • $$1.5,0.5$$
  • $$1,1$$
  • $$-0.5,2.5$$
Solve:
$$4x + \frac{6}{y} = 15$$
$$6x - \frac{8}{y} = 14$$
  • $$x=-3,y=2$$
  • $$x=2,y=3$$
  • $$x=3,y=-2$$
  • $$x=3,y=2$$
 Solve for $$x$$ and $$y$$ by using method of substitution :
$$0.2x+0.3y=1.3$$; $$0.4x+0.5y=2.3$$
  • $$-2,-3$$
  • $$2,-3$$
  • $$2,3$$
  • $$-2,3$$
To eliminate x, from $$3x+y=7$$ and $$-x+2y=2$$ second equation is multiplied by ______
  • $$1$$
  • $$3$$
  • $$2$$
  • $$-1$$
Solve 
$$5x-4y+8=0$$
$$7x+6y-9=0$$.
  • $$x = \cfrac{6}{29}$$ and $$y = -\cfrac{101}{58}$$

  • $$x = -\cfrac{6}{29}$$ and $$y = \cfrac{101}{58}$$

  • $$x = -\cfrac{8}{29}$$ and $$y = \cfrac{101}{58}$$

  • None of these
Find the value of $$x$$ and $$y$$ using substitution method:
$$x-  y = 2$$ and $$2x - y = 9$$
  • $$7$$ and $$7$$
  • $$7$$ and $$5$$
  • $$-7$$ and $$-5$$
  • $$5$$ and $$7$$
Solve : $$ ax + by = a - b$$
             $$bx - ay = a + b$$
  • $$x=a,y=-b$$
  • $$x=1,y=-1$$
  • $$x=-1,y=1$$
  • $$x=\dfrac {1}{a},y=-\dfrac {1}{b}$$
Solve $$0.2x+0.3y=1.3$$ 
$$0.4x+0.5y=2.3$$
  • $$x=-2$$ and $$y=3$$
  • $$x=3$$ and $$y=3$$
  • $$x=2$$ and $$y=3$$
  • None of these
Given two straight lines $$x + y - 7 = 0$$ and $$x - y + 3 = 0$$ . Find point of intersection of them.
  • $$(2,5)$$
  • $$(-2,-5)$$
  • $$(2,-5)$$
  • $$(-2,5)$$
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