Question 1

Which of the following is a linear equation in two variables?

Accepted Answer

A linear equation in two variables is an equation that can be written in the form $ax + by + c = 0$, where $a, b,$ and $c$ are real numbers and $a 
eq 0, b 
eq 0$, and the degrees of both variables $x$ and $y$ are 1. Looking at the options, $2x + 3y = 5$ satisfies this definition.

Question 2

How many solutions does a linear equation in two variables have?

Accepted Answer

A linear equation in two variables has infinitely many solutions because every point on the line representing the equation is a solution to the equation.

Question 3

The graph of the equation $x + y = 4$ intersects the x-axis at which point?

Accepted Answer

To find the intersection with the x-axis, we put $y = 0$ in the equation $x + y = 4$, which gives $x + 0 = 4 \implies x = 4$. Thus, the point of intersection is $(4, 0)$.

Question 4

If $(2, 1)$ is a solution of the equation $2x + 3y = k$, then the value of $k$ is:

Accepted Answer

Substitute $x = 2$ and $y = 1$ into the equation $2x + 3y = k$. We get $2(2) + 3(1) = k \implies 4 + 3 = k \implies k = 7$.

Question 5

The equation of the x-axis is:

Accepted Answer

On the x-axis, the y-coordinate of every point is zero. Therefore, the equation of the x-axis is $y = 0$.

Linear Equations in Two Variables