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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]

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