LINEAR EQUATION QUESTIONS FOR SSC GD PDF<\/a><\/p>\n GET 20 SSC GD MOCK FOR JUST RS.117<\/a><\/p>\n FREE SSC EXAM YOUTUBE VIDEOS<\/a><\/p>\n Question 1:\u00a0<\/b>A linear equation has 4 variables. What is the least number of equations do you need to figure out the values of all 4 variables?<\/p>\n a)\u00a02<\/p>\n b)\u00a03<\/p>\n c)\u00a04<\/p>\n d)\u00a05<\/p>\n e)\u00a08<\/p>\n Question 2:\u00a0<\/b>Solve the following system of linear equations and determine the value of x + y + z. a)\u00a020<\/p>\n b)\u00a010<\/p>\n c)\u00a05<\/p>\n d)\u00a015<\/p>\n e)\u00a0Cannot be determined<\/p>\n Question 3:\u00a0<\/b>At least how many equations are required to determine the values of all the variables in a linear equation with 3 variables<\/p>\n a)\u00a01<\/p>\n b)\u00a02<\/p>\n c)\u00a03<\/p>\n d)\u00a04<\/p>\n e)\u00a05<\/p>\n Question 4:\u00a0<\/b>How many solutions do the following set of equations have? a)\u00a0Unique solution<\/p>\n b)\u00a0No solution<\/p>\n c)\u00a0Infinite solutions<\/p>\n d)\u00a0Cannot be determined<\/p>\n e)\u00a0None of these<\/p>\n Question 5:\u00a0<\/b>How many solutions do the following set of equations have? a)\u00a0Unique solution<\/p>\n b)\u00a0No solution<\/p>\n c)\u00a0Infinite solutions<\/p>\n d)\u00a0Cannot be determined<\/p>\n e)\u00a0None of these<\/p>\n SSC GD FREE PREVIOUS PAPERS<\/a><\/p>\n SSC GD FREE MOCK TEST 2019<\/a><\/p>\n Question 6:\u00a0<\/b>How many solutions do the following set of equations have? a)\u00a0Unique solution<\/p>\n b)\u00a0No solution<\/p>\n c)\u00a0Infinite solutions<\/p>\n d)\u00a0Cannot be determined<\/p>\n e)\u00a0None of these<\/p>\n Question 7:\u00a0<\/b>The number obtained by interchanging the digits of a two-digit number is less than the original number by 63 If the sum of the digits of the number is 11, what is the original number ?<\/p>\n a)\u00a029<\/p>\n b)\u00a092<\/p>\n c)\u00a074<\/p>\n d)\u00a0Cannot be determined<\/p>\n e)\u00a0None of these<\/p>\n Question 8:\u00a0<\/b>Two linear equations 3x+5y=20, 24x+40y=K will have no solution for x and y when k = ?<\/p>\n a)\u00a0160<\/p>\n b)\u00a08<\/p>\n c)\u00a040<\/p>\n d)\u00a0both b and c<\/p>\n Question 9:\u00a0<\/b>x+3y=12 and 5x+15y=3k are two linear equations then for what value of k will the equations have infinite solutions ?<\/p>\n a)\u00a00<\/p>\n b)\u00a04<\/p>\n c)\u00a020<\/p>\n d)\u00a012<\/p>\n Question 10:\u00a0<\/b>How many solutions does a pair of linear equations will have, if the equations are a)\u00a00<\/p>\n b)\u00a01<\/p>\n c)\u00a02<\/p>\n d)\u00a0Infinite<\/p>\n DOWNLOAD HIGHLY RATED SSC APP<\/a><\/p>\n Answers & Solutions:<\/strong><\/span><\/p>\n 1)\u00a0Answer\u00a0(C)<\/strong><\/p>\n To uniquely determine each of the given variable, we need the number of equations to be at least equal to the number of variables. Hence for 4 variables, we need at least 4 equations to uniquely determine the value of each variable.<\/p>\n 2)\u00a0Answer\u00a0(D)<\/strong><\/p>\n 3x + 2y + z = 25 (I) 3)\u00a0Answer\u00a0(C)<\/strong><\/p>\n In a linear equation with 3 variables, we will have 3 unknowns and so we will need at least 3 equations to uniquely determine the value of all three variables.<\/p>\n 4)\u00a0Answer\u00a0(C)<\/strong><\/p>\n The two linear equations, $ a_{1}x+b_{1}y=c1$ and $ a_{2}x+b_{2}y=c2$ : 5)\u00a0Answer\u00a0(B)<\/strong><\/p>\n The two linear equations, $ a_{1}x+b_{1}y=c1$ and $ a_{2}x+b_{2}y=c2$ :
\n3x + 2y + z = 25
\n5x + 3y + z = 40
\nx + 4y + 2z = 10<\/p>\n
\n$2x+3y=9$ and $4x+6y=18$<\/p>\n
\n$2x+3y=9$ and $4x+6y=27$<\/p>\n
\n$2x+3y=9$ and $3x+2y=9$<\/p>\n
\n7x+4y-16=0 and 14x+6y-32=0?<\/p>\n
\n5x + 3y + z = 40 (II)
\nx + 4y + 2z = 10 (III)
\nII – I gives
\n2x + y = 15 (IV)
\n2*(I) – III gives
\n5x = 40
\n=> x = 8
\nPutting value of x in equation IV gives
\ny = -1
\nPutting value of x and y in I gives z = 3
\nSo required sum is 8+3-1 = 10<\/p>\n
\nHave a unique solution if $\\frac{a_{1}}{a_{2}}\\neq\\frac{b_{1}}{b_{2}}$
\nHave no solution if $\\frac{a_{1}}{a_{2}}=\\frac{b_{1}}{b_{2}}\\neq\\frac{c_{1}}{c_{2}}$
\nHave infinite solutions if $\\frac{a_{1}}{a_{2}}=\\frac{b_{1}}{b_{2}}=\\frac{c_{1}}{c_{2}}$
\nIn the given equations $\\frac{2}{4}=\\frac{3}{6}=\\frac{9}{18}$. So the equations have infinite solutions.<\/p>\n
\nHave a unique solution if $\\frac{a_{1}}{a_{2}}\\neq\\frac{b_{1}}{b_{2}}$
\nHave no solution if $\\frac{a_{1}}{a_{2}}=\\frac{b_{1}}{b_{2}}\\neq\\frac{c_{1}}{c_{2}}$
\nHave infinite solutions if $\\frac{a_{1}}{a_{2}}=\\frac{b_{1}}{b_{2}}=\\frac{c_{1}}{c_{2}}$
\nIn the given equations $\\frac{2}{4}=\\frac{3}{6}\\neq\\frac{9}{27}$. So the equations have no solution.<\/p>\n