Q.1 (A)(i) For solving the simultaneous equations \(x + y = 3\), \(3x - 2y = 4\). Find the value of determinant D.
Linear Equations in Two Variables
Linear Equations in Two Variables
Every question from past board papers on Linear Equations in Two Variables, newest paper first. Open any question for its full worked answer.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper June 2026
Full paper →-
-
Q.1 (B)(i) If \(15x + 17y = 21\) and \(17x + 15y = 11\), then find the value of \(x + y\).
-
Q.2 (A)(i) Complete the following table to draw the graph of equation \(x - y = 1\).
Activity :
\(x\) 0 ____ ____ \(y\) ____ 0 –3 \((x, y)\) (0, –1) ____ (–2, –3) -
Q.2 (B)(i) Solve the following simultaneous equations : \(5x + 3y = 9\); \(2x - 3y = 12\)
-
Q.3 (B)(i) Solve the following simultaneous equations by Cramer’s rule : \(x + 2y = -1\); \(2x - 3y = 12\)
-
Q.5 (i) If the point (2, 1) lies on the graph of the equation \(x + ay = 4\), then find the value of ‘a’ and draw the graph of the equation so obtained.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2026
Full paper →-
Q.1 (A)(iii) To draw graph of \(4x + 5y = 19\), find the value of \(y\) when \(x = 1\).
-
Q.1 (B)(ii) For simultaneous equations in variables \(x\) and \(y\), if \(D_x = -42\) and \(D = -3\), then find the value of \(x\).
-
Q.2 (A)(iii) Complete the following table to draw graph of the equation.
\[ x + y = 3 \]
\(x\) 3 ____ \(y\) ____ 5 \((x, y)\) ____ ____ -
Q.2 (B)(ii) Solve the following simultaneous equations :
\[ x + y = 4 \]
\[ 2x - y = 2 \]
-
Q.3 (B)(i) Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.
-
Q.5 (ii) There are some students in group A and group B. If one student goes from group A to group B, then the number of students in both groups is same. But one student goes from group B to group A, then the number of students in group A becomes twice of group B. Find the number of students in each group.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2025
Full paper →-
Q.1 (A)(i) \(\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}\). Write the degree of the given determinant.
-
Q.1 (B)(i) If 2x + y = 7 and x + 2y = 11, then find the value of x + y.
-
Q.2 (A)(i) Complete the following table to draw the graph of x + 2y = 4.
Activity :
x –2 ____ y ____ 1 (x, y) ____ ____ -
Q.2 (B)(i) Solve the following simultaneous equations : x + y = 3; 3x – 2y = 4
-
Q.3 (B)(i) Solve the following simultaneous equations by Cramer’s rule : 4x + 3y = 18; 3x – 2y = 5
-
Q.5 (i) Draw the graphs representing the equation 2x = y + 2 and 4x + 3y = 24 on the same graph paper. Find the area of the triangle formed by these lines and the X-axis.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper July 2025
Full paper →-
Q.1 (A)(i) The value of determinant \(\begin{vmatrix} 5 & 3 \\ -7 & -4 \end{vmatrix}\) is ..........................
-
Q.1 (B)(i) For simultaneous equations in variables \(x\) and \(y\), \(D_x = 49\), \(D_y = -63\), \(D = 7\), then find the value of \(x\).
-
Q.2 (B)(i) Find the values of \((x + y)\) and \((x - y)\) of the following given simultaneous equations :
\(101x + 99y = 501\)
\(99x + 101y = 499\)
-
Q.3 (B)(iv) Solve the following simultaneous equations graphically : \(x + y = 6\), \(x - y = 4\)
-
Q.4 (i) In an agriculture field the ratio of salary of skilled and unskilled workers is 5 : 4. Total salary of one day of both of them is ₹ 900. Find daily wages of skilled and unskilled workers.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper July 2024
Full paper →-
Q.1 (A)(i) For simultaneous equations in variables \(x\) and \(y\), \(D_x = 49\), \(D_y = -63\), \(D = 7\), then what is the value of \(x\) ?
-
Q.1 (B)(i) Find the value of the following determinant : \(\begin{vmatrix} 5 & -2 \\ -3 & 1 \end{vmatrix}\).
-
Q.2 (A)(i) Complete the following table for drawing the graph of the equation : \(x + 2y = 4\)
\(x\) –2 0 ____ \(y\) ____ 2 1 \((x, y)\) ____ (0, 2) ____ -
Q.2 (B)(i) Solve the following simultaneous equations : \(x + y = 5\); \(x - y = 3\)
-
Q.3 (B)(i) Solve the following simultaneous equation by Cramer’s method : \(4m - 2n = -4\); \(4m + 3n = 16\).
-
Q.5 (ii) Using information given in the following figure, find the length and breadth of this rectangle in cm.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2024
Full paper →-
Q.1 (A)(ii) To draw the graph of \(x + 2y = 4\), find \(x\) when \(y = 1\) :
-
Q.1 (B)(i) If \(17x + 15y = 11\) and \(15x + 17y = 21\), then find the value of \(x - y\).
-
Q.2 (A)(i) If (0, 2) is the solution of \(2x + 3y = k\), then to find the value of \(k\), complete the following activity :
Activity :
(0, 2) is the solution of the equation \(2x + 3y = k\).
Put \(x\) = ____ and \(y\) = ____ in the given equation;
\(\therefore 2 \times\) ____ \(+ 3 \times 2 = k\)
\(\therefore 0 + 6 = k\)
\(\therefore k\) = ____
-
Q.2 (B)(i) \(\square\)ABCD is a rectangle. Write two simultaneous equations using information given below in the diagram, in the form of \(ax + by = c\) :
-
Q.3 (B)(ii) Solve the following simultaneous equations using Cramer's rule :
\(3x - 4y = 10\), \(4x + 3y = 5\)
-
Q.5 (ii) Draw the graph of the equation \(x + y = 4\) and answer the following questions :
(a) Which type of triangle is formed by the line with X and Y-axes based on its sides.
(b) Find the area of that triangle.