Question

How many solutions is there \[y = 13x + 8\]?

Answer 1

Hint: Here in this question, we have to tell how many solutions will get when the given equation. The given equation in the form of equation of straight line or linear equation i.e., \[y = mx + b\] to solve this while giving a x values like 0, 1, 2, 3, … on simplification simultaneously we get the y values

Complete step-by-step answer:
The given equation is a linear equation. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation. The general representation of the straight-line equation is \[y = mx + b\], it involves only a constant term and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, this equation is called a "linear equation of two variables," where y and x are the variables.
Consider the given equation
\[ \Rightarrow \,\,\,\,y = 13x + 8\]
To solve this, we have to give x value as \[x = 0,1,2,3,...,\infty \]
At \[x = 0\], then
\[ \Rightarrow \,\,\,\,y = 13\left( 0 \right) + 8 = 8\]
At \[x = 1\], then
\[ \Rightarrow \,\,\,\,y = 13\left( 1 \right) + 8 = 21\]
At \[x = 2\]
\[ \Rightarrow \,\,\,\,y = 13\left( 2 \right) + 8 = 34\]
So on, continuing like this up to \[x = \infty \].
Hence, the given linear equation \[y = 13x + 8\] gives infinitely many solutions.

Note: The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the tables of multiplication, we can solve the equation.