Connect with a global community of knowledgeable individuals on IDNLearn.com. Find accurate and detailed answers to your questions from our experienced and dedicated community members.
We have to solve the following system of equations:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ 2x-3y=4 \end{gathered}[/tex]We have to graph the equations and, as they are written in standard form, we are going to calculate the intercepts for both.
We will write the equations in slope-intercept form.
For the first equation we have:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ \frac{3}{4}y=-\frac{1}{2}x+1 \\ y=\frac{4}{3}(-\frac{1}{2}x+1) \\ y=-\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]For the second equation we have:
[tex]\begin{gathered} 2x-3y=4 \\ 2x-4=3y \\ y=\frac{1}{3}(2x-4) \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Both slopes are different, what means that the lines are not parallel and will intersect, so we already know that the system is independent.
Using the slopes and the y-intercepts, we can graph the equations as:
The solution to the system is the intersection point which is (2,0).
Answer:
The system is independent and its solution is (x,y) = (2,0)
