List of top Mathematics Questions on Linear Equations asked in CBSE Class X

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

The value of \(k\) for which the system of linear equations \(\frac{x}{2} + \frac{y}{3} = 5\) and \(2x + ky = 7\) is inconsistent, is

Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.

If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

Determine graphically, the coordinates of vertices of a triangle whose equations are \(2x - 3y + 6 = 0\); \(2x + 3y - 18 = 0\) and \(x = 0\). Also, find the area of this triangle.

Draw the graph of the pair of linear equations $x - y + 2 = 0$ and $4x - y - 4 = 0$. Calculate the area of the triangle formed by the lines so drawn and the $x$-axis.

The system of linear equations \(px + qy = r\) and \(p_1x + q_1y = r_1\) has a unique solution, if :

The system of equations \(x = 2\) and \(x = 3\) has:

Solve the following system of equations graphically : \(x + 3y = 6\) and \(2x - 3y = 12\). Also, find the area of the triangle formed by the lines \(x + 3y = 6\), \(x = 0\) and \(y = 0\).

One of the supplementary angles exceeds the other by 120°. Express this as a system of linear equations and find the angles.

Nidhi received simple interest of ₹1,200 when she invested ₹x at 6% per annum and ₹y at 5% per annum for 1 year. Had she invested ₹x at 3% per annum and ₹y at 8% per annum for that year, she would have received simple interest of ₹1,260.Find the values of x and y.

Solve the following pair of equations algebraically:
\[ 101x + 102y = 304 \quad \text{(i)}\\ 102x + 101y = 305 \quad \text{(ii)} \]

Solve the following pair of linear equations by graphical method : \(2x + y = 9\) and \(x - 2y = 2\).

Check whether the following pair of equations is consistent or not. If consistent, solve graphically:
\[ x + 3y = 6\\ 3y - 2x = -12 \]

Check whether the following system of equations is consistent or not. If consistent, solve graphically: \[ x - 2y + 4 = 0, \quad 2x - y - 4 = 0 \]

The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.

The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.