Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

What is the solution to the system?

Line 1
x y
–2 –4
–1 –1
Line 2
x y
2 3
3 1

( , )

Sagot :

naǫ
Line 1:
[tex]x_1=-2 \\ y_1=-4 \\ \\ x_2=-1 \\ y_2=-1 \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-4)}{-1-(-2)}=\frac{-1+4}{-1+2}=\frac{3}{1}=3 \\ \\ y=3x+b \\ (-1,-1) \\ -1=3 \times (-1)+b \\ -1=-3+b \\ -1+3=b \\ b=2 \\ \\ y=3x+2[/tex]

Line 2:
[tex]x_1=2 \\ y_1=3 \\ \\ x_2=3 \\ y_2=1 \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{3-2}=\frac{-2}{1}=-2 \\ \\ y=-2x+b \\ (3,1) \\ 1=-2 \times 3+b \\ 1=-6+b \\ 1+6=b \\ b=7 \\ \\ y=-2x+7[/tex]

The system of equations is:
[tex]y=3x+2 \\ y=-2x+7 \\ \\ y=y \\ 3x+2=-2x+7 \\ 3x+2x=7-2 \\ 5x=5 \\ x=\frac{5}{5} \\ x=1 \\ \\ y=3x+2=3 \times 1+2=3+2=5 \\ \\ \boxed{(x,y)=(1,5)}[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.