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Important Questions: Test of consistency and solution of simultaneous linear equations in two or three variables using matrices for JEE

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Q1MathsUnit 3: Matrices and Determinants
If 2a=b,2 a=b, the pair of equations ax+a x+ by=2a2−3b2,x+2y=2a−6bb y=2 a^{2}-3 b^{2}, x+2 y=2 a-6 b possess
Q2MathsUnit 3: Matrices and Determinants
The addition of two numbers is −72.-72 . If one number is thrice the another number. Find the greater number
Q3MathsUnit 3: Matrices and Determinants
Solve the following equations by substitution method. x=2y−1;y=2x−7\boldsymbol{x}=\mathbf{2} \boldsymbol{y}-\mathbf{1} ; \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{7}
Q4MathsUnit 3: Matrices and Determinants
Dashrath and Naresh are friends ,Naresh is 2 years younger than Dashrath.If the sum of their age is 56 years, find their present age.
Q5MathsUnit 3: Matrices and Determinants
The ratio of income of two persons is 9: 7 and the ratio of their expenditure is 4:3.4: 3 . If each of them manages to save Rs. 2000 per month, find their monthly income.
Q6MathsUnit 3: Matrices and Determinants
Solve the following pair of linear (simultaneous) equations by the method of elimination: 8x+5y=98 x+5 y=9 3x+2y=4\mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{4}
Q7MathsUnit 3: Matrices and Determinants
Solve the following pair of equations: ax−by=0\frac{a}{x}-\frac{b}{y}=0 ab2x+a2by=a2+b2\frac{a b^{2}}{x}+\frac{a^{2} b}{y}=a^{2}+b^{2}
Q8MathsUnit 3: Matrices and Determinants
A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number

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What makes a Test of consistency and solution of simultaneous linear equations in two or three variables using matrices question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

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