PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - True/False

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Q 01 / 25
Any equation of the form \(ax + by + c = 0\) with \(a\) and \(b\) not both zero is called a linear equation in two variables.
Q 02 / 25
The equation \(7x - 5 = 0\) is not a linear equation in two variables because it contains only one variable.
Q 03 / 25
The solution of a pair of linear equations in two variables is the ordered pair \((x,y)\) that satisfies both equations simultaneously.
Q 04 / 25
Graphically, the solution of a pair of linear equations in two variables corresponds to the point of intersection of the two lines.
Q 05 / 25
A pair of linear equations in two variables can have exactly two distinct solutions.
Q 06 / 25
If the graphs of two linear equations are parallel lines, then the pair is inconsistent.
Q 07 / 25
If the graphs of two linear equations coincide, then the pair has infinitely many solutions.
Q 08 / 25
If a pair of linear equations has a unique solution, then their graphs must be parallel lines.
Q 09 / 25
For two equations \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\), if \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\), then the pair is consistent with a unique solution.
Q 10 / 25
For the same pair, if \(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\), then the equations represent coincident lines.
Q 11 / 25
If \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\), then the pair of linear equations has infinitely many solutions.
Q 12 / 25
The substitution method of solving a pair of linear equations involves eliminating one variable by adding the equations directly without any prior step.
Q 13 / 25
In the elimination method, the coefficients of one variable are made equal (or opposites) so that adding or subtracting the equations removes that variable.
Q 14 / 25
The cross-multiplication method can be used when the pair of linear equations has a unique solution.
Q 15 / 25
If the pair of equations is inconsistent, the cross-multiplication formula will involve division by zero.
Q 16 / 25
The pair of equations \(x = 3\) and \(y = 2\) represents two lines which intersect at the point \((3,2)\).
Q 17 / 25
The equation of any vertical line in the coordinate plane can be written in the form \(y = k\), where \(k\) is a constant.
Q 18 / 25
If a word problem leads to two linear equations in the same two variables, solving the pair gives the required answer to the problem.
Q 19 / 25
In a pair of linear equations, changing both equations by multiplying them with the same non-zero constant does not change the solution of the system.
Q 20 / 25
In the graphical method, it is enough to plot just one point for each equation to draw its line accurately.
Q 21 / 25
If the pair of equations has infinitely many solutions, then every solution of one equation is also a solution of the other.
Q 22 / 25
For the pair \(2x + 3y = 6\) and \(4x + 6y = 10\), the lines are coincident.
Q 23 / 25
If two linear equations in two variables have the same left-hand side but different constants on the right-hand side, the pair is always inconsistent.
Q 24 / 25
Every pair of linear equations in two variables can be solved only by algebraic methods, not by graphs.
Q 25 / 25
If the solution of a pair of linear equations is given as \(x = 0\) and \(y = -1\), then the ordered pair \((0, -1)\) will lie on the graphs of both equations.
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