To determine if the lines of the equation system are parallel, perpendicular, equal, or not perpendicular, the first step is to write both equations in the slope-intercept form:
Equation 1
[tex]6x-15y=15[/tex]To write this equation in slope-intercept form, the first step is to pass the x-term 6x to the right side of the equation. For this, apply the opposite operation to both sides of it:
[tex]\begin{gathered} 6x-6x-15y=-6x+15 \\ -15y=-6x+15 \end{gathered}[/tex]The next step is to divide both sides by -15:
[tex]\begin{gathered} -\frac{15y}{-15}=-\frac{6x}{-15}+\frac{15}{-15} \\ y=\frac{2}{5}x-1 \end{gathered}[/tex]Equation 2:
This equation is already written on the slope-intercept form:
[tex]y=\frac{2}{5}x-1[/tex]As you can see both equations are equal, this means that this equation system has infinite solutions.
