List of top Mathematics Questions on Linear Equations

The pair of linear equations $x-y-1=0$ and $x-2y+2=0$ represents _____ lines.
If the sum of two numbers is 8 and their difference is 2, then those two numbers are _____.
If two linear equations represent the same line, then the pair of linear equations has _____.
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.
Loan at 12% SI for 3 years gives Rs. 5400 interest. Find principal.
The sum of the first \(10\) terms of an A.P. is \(150\). If the first term is \(10\), what is the common difference?
The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has
Find \(x\): \(2x + 3 = 7x - 8\).
Find \(x\): \(4(x - 2) = 3(x + 5)\).
Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.
Evaluate the series \[ \frac{1}{25!}+\frac{1}{3!\,23!}+\frac{1}{5!\,21!}+\cdots \text{ up to 13 terms.} \]
Find the number of real solutions of \[ x|x-3|+|x-1|+3=0 \]
Find the sum of all real solutions of
$|x + 1|^2 - 4|x + 1| + 3 = 0$
The sum of a two-digit number and the number obtained by reversing the digits is 110. If the tens digit of the number is 6 more than the units digit, then find the number.

Solve the following pairs of linear equations : $3x - 5y = 4$, $9x = 2y + 7$
In linear equation $\frac{x}{3} + \frac{y}{2} = 6$ if $x = 9$ then the value of $y$ will be :
Consider a geometric sequence $729,\,81,\,9,\,1,\ldots$ If $P_n$ denotes the product of first $n$ terms of the G.P. such that \[ \sum_{n=1}^{40} (P_n)^{\frac{1}{n}}=\frac{3^{\alpha}-1}{2\times 3^{\beta}}, \] then find the value of $(\alpha+\beta)$.
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
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 \(y = 0\).