To determine the degree of the given linear equations, we must first understand what a "degree" means in the context of algebraic equations.
The degree of an equation is defined as the highest power of any variable in the equation. For example, in a quadratic equation like [tex]\( ax^2 + bx + c = 0 \)[/tex], the highest power of the variable [tex]\( x \)[/tex] is 2, so the degree of the quadratic equation is 2.
Given your equations:
1. [tex]\( 3x + 2y - 8 = 0 \)[/tex]
2. [tex]\( x + 2y - 8 = 0 \)[/tex]
Let's analyze each equation individually.
For the first equation:
[tex]\[ 3x + 2y - 8 = 0 \][/tex]
Here, the terms are [tex]\( 3x \)[/tex], [tex]\( 2y \)[/tex], and [tex]\( -8 \)[/tex]. Each term involving the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is raised to the power of 1. Therefore, the highest power of any variable in this equation is 1. Thus, the degree of this equation is 1.
For the second equation:
[tex]\[ x + 2y - 8 = 0 \][/tex]
In this case, the terms are [tex]\( x \)[/tex], [tex]\( 2y \)[/tex], and [tex]\( -8 \)[/tex]. Similar to the first equation, each term involving the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is raised to the power of 1. Therefore, the highest power of any variable in this equation is also 1. Thus, the degree of this equation is 1.
For both equations, we observe that the highest power of the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is 1. Therefore, the degree of these linear equations is:
[tex]\[ \boxed{1} \][/tex]
This conclusion matches our earlier explanation about the degrees of linear equations.
