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2. Which of the following is not a linear equation?

(a) [tex]2x + 5 = 1[/tex]

(b) [tex]x - 1 = 0[/tex]

(c) [tex]y + 1 = 0[/tex]

(d) [tex]5x + 3[/tex]


Sagot :

To determine which of the following expressions is not a linear equation, we need to understand the definition of a linear equation. A linear equation is an equation of the form [tex]\(Ax + B = 0\)[/tex] or [tex]\(Ax + By + C = 0\)[/tex], where [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are constants, and [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are variables.

Let's analyze each option:

(a) [tex]\(2x + 5 = 1\)[/tex]

We can rewrite this equation to fit the standard form:
[tex]\[2x + 5 - 1 = 0\][/tex]
[tex]\[2x + 4 = 0\][/tex]
This is a standard linear equation.

(b) [tex]\(x - 1 = 0\)[/tex]

This fits the form [tex]\(Ax + B = 0\)[/tex] directly:
[tex]\[x - 1 = 0\][/tex]
This is a linear equation.

(c) [tex]\(y + 1 = 0\)[/tex]

This can also be written as:
[tex]\[y + 1 = 0\][/tex]
It also fits the linear equation form.

(d) [tex]\(5x + 3\)[/tex]

This is an expression rather than an equation because it doesn't have an equality sign ('=') and cannot be written in the form [tex]\(Ax + B = 0\)[/tex]:

Given this analysis, the option that is not a linear equation is:

(d) [tex]\(5x + 3\)[/tex]