Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Use algebra to find the point at which the line


intersects the line


.

Use Algebra To Find The Point At Which The Line Intersects The Line class=

Sagot :

Answer:

[tex](3\ ,\ \frac{17}{4})[/tex]

Step-by-step explanation:

  • To find the intersection point you need to set the two equations equal to each other and solve for x .

here is how to do it :

[tex]$\begin{aligned} & -\frac{2}{3} x+\frac{9}{4}=\frac{7}{5} x+\frac{169}{20} \\ & \Leftrightarrow-\frac{2}{3} x-\frac{7}{5} x=\frac{169}{20}-\frac{9}{4} \\ & \Leftrightarrow \frac{-10 x-21 x}{15}=\frac{169-45}{20} \\ & \Leftrightarrow-\frac{31}{15} x=\frac{124}{20} \\ & \Leftrightarrow x=\frac{124}{20} \times\left(-\frac{15}{31}\right) \\ & \Leftrightarrow x=-\frac{1860}{620} \\ & \Leftrightarrow x=-3\end{aligned}$[/tex]

  • Now, you can plug it back into either of the original equations to find y.

let’s use g(x) :

[tex]$\begin{aligned} g(-3) & =-\frac{2}{3} \times(-3)+\frac{9}{4} \\ & =2+\frac{9}{4} \\ & =\frac{8+9}{4} \\ & =\frac{17}{4} \\ & =4.25\end{aligned}$[/tex]

Therefore, the coordinates of the intersection points are :

[tex](3\ ,\ \frac{17}{4})[/tex]

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.