Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
The Slope-Intercept form of an equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
- The first equation given in the exercise is:
[tex]4x+3y=5[/tex]Solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 3y=-4x+5 \\ y=-\frac{4}{3}x+\frac{5}{3} \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_1=-\frac{4}{3} \\ \\ b_1=\frac{5}{3} \end{gathered}[/tex]- The second equation is:
[tex]24x+3y=7[/tex]Solve for "y":
[tex]\begin{gathered} 3y=-24x+7 \\ \\ y=\frac{-24}{3}x+\frac{7}{3} \\ \\ y=-8x+\frac{7}{3} \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_2=-8 \\ \\ b_2=\frac{7}{3} \end{gathered}[/tex]- As you can notice, the lines are not parallel, because:
[tex]m_1\ne m_2[/tex]- The lines are not the the same line, because:
[tex]\begin{gathered} m_1\ne m_2 \\ b_1\ne b_2 \end{gathered}[/tex]- Therefore, since they are different ant they're not parallel, they will intersect each other at some point. This means that the System of equations has one solution.
The answer is: Option b.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
