Question

For the equation \[x + 2y = 8\] find the solution which represents a point on
A) x-axis
B) y-axis

Answer 1

Hint: We will first analyze the definition of the linear equation and their examples. We will put the value of y equals to zero to find the point on x-axis. We will then put the value of x equals to zero to find the point on y axis in the equation \[x + 2y = 8\]

Complete step-by-step answer:
Linear equations are first-order equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). There might be more than one variable in a linear equation. If there are two variables in a linear equation, it is referred to as linear equations in two variables, and so on.
Examples of Linear Equation in two variables are y+7x=3, 3a+2b = 5, 6x+9y-12=0
We know that the Standard form of a linear equation in two variables is represented as ax + by + c = 0, where, a ≠ 0, b ≠ 0 , x and y are the variables.
We know that the point which lies on the x-axis has its ordinate is 0.
So, we will find the solution for first problem by putting y=0 in the equation \[x + 2y = 8\]
$ \Rightarrow x + 2y = 8$
We will put y equals to 0
\[ \Rightarrow x + 2 \times 0 = 8\]
\[ \Rightarrow x = 8\]
So, the point is (8,0)
We will now find the solution of second question
We know that the point which lies on the y-axis has its abscissa 0.
We will put the value of x equals to zero in equation \[x + 2y = 8\]
$ \Rightarrow x + 2y = 8$
We will put x equals to 0
\[ \Rightarrow 0 + 2y = 8\]
We will divide the equation by 2
\[ \Rightarrow 2y = 8\]
So , the point is (0,4)
Hence, the point when equation \[x + 2y = 8\] has x and y axis as zero respectively are (8,0), (0,4)

Note: We should be familiar with the linear equation and its behavior. For solving questions of linear equations, it is very important how we plot the equation and make the use of graphs. We should always first plot the equation on a graph, it will help a lot.