Number of Solutions of a Linear Equation in Two Variable

Q. How many solutions do a linear equation of two variables has?

1. One.
2. Finite number of solutions.
3. Infinite number of solutions.
4. None of the above.

Q.

The joint equation of the straight lines $x+y=1$ and $x-y=4$, is

1. $x^2-y^2=-4$

2. $x^2-y^2=4$

3. $\left(x+y-1\right)\left(x-y-4\right)$

4. $\left(x+y+1\right)\left(x-y+4\right)$

Q.

Write the equation of three lines passing through$(2,–3)$.

Q.

When solving a system of equations graphically, when would you need to estimate the solution?

Q. A carpenter can make maximum $6$ tables or $2$ chairs in a day. Generate the linear equation and find the different combinations of furniture he can make in a day, given that there is no unfinished work at the end of the day.

1. $6$ tables and no chairs.
2. $2$ chairs and no tables.
3. $3$ tables and $1$ chair.
4. $6$ tables and $2$ chair.

Q.

Give equation of two lines passing through $\left(2,14\right)$. How many more such lines are there$?$ and why$?$

Q.

Give the geometric representation of the linear equation: $y=3$ as in two variables.

Q. Find the number of solutions which are common to both $y=8x+3\&5y-x=1,$ if any.

Q. The pair of straight lines $x+y=2$ and $x=-2y+6$ have

1. One solution
2. Two solutions
3. No solution
4. Infinite solutions

Q. Find the number of solution(s) of $\sqrt{2}y+\frac{x}{\sqrt[3]{35}}=3\sqrt{3}$ for $x=45.$

1. One.
2. Two.
3. Infinitely Many.
4. This is not a linear equation.

Q. What is the number of solutions for the given system of linear equations $y=2x+3$ and $x+y=1$?

1. One
   
2. Two
3. Infinite
4. No solution

Q. Find the number of integer values of y-coordinate as solutions of the equation $y=\frac{1}{2}x+5$ between $x=-1$ and $x=3.$

1. One.
2. Two.
3. Three.
4. Infinitely many.

Q. $y=3x-2$ is the equation for a line.
Match the following with the support of the above statement.

1. $3$
2. -2
3. $2$
4. 1