Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

The line with equation ax+by=20 passes through the points(-2,10) and (1,5)
find a and b

Sagot :

Lilith
[tex]ax+by=20 \\ \\(-2,10) \\ \\ a*(-2)+b*10 = 20 \\ \\-2a +10b = 20 \\ \\ (1,5)\\ \\ a*1+b*5 = 20 \\ \\ a +5b = 20[/tex]
 
[tex]\begin{cases} -2a+10b =20\\ a+5b =20 \ /*2\end{cases} \\ \\\begin{cases} -2a+10b =20\\ 2a+10b =40 \end{cases}\\--------\\ 20b=60 \ / :20 \\ \\b=\frac{60}{20} =3[/tex]

[tex]-2a+10b=20 \\ \\-2a +10*3=20 \\ \\-2a +30=20\\ \\-2a=20-30\\ \\-2a=-10 \ /: (-2)[/tex]

[tex]a=\frac{10}{2}=5\\ \\\begin{cases} a= 5 \\b=3\end{cases}[/tex]
[tex]ax+by=20\\\\for\ (-2;\ 10)\to x=-2;\ y=10\ substitute\\\\-2a+10b=20\\\\for\ (1;\ 5)\to x=1;\ y=5\ substitute\\\\1a+5b=20\\\\\\ \left\{\begin{array}{ccc}-2a+10b=20&/:2\\a+5b=20\end{array}\right[/tex]
[tex]+\left\{\begin{array}{ccc}-a+5b=10\\a+5b=20\end{array}\right\\------------\\.\ \ \ \ \ \ \ 10b=30\ \ \ \ /:10\\.\ \ \ \ \ \ \ \ b=3\\\\\left\{\begin{array}{ccc}b=3\\a+5b=20\end{array}\right\\\left\{\begin{array}{ccc}b=3\\a+5\cdot3=20\end{array}\right\\\left\{\begin{array}{ccc}b=3\\a+15=20\end{array}\right\\\left\{\begin{array}{ccc}b=3\\a=20-15\end{array}\right\\\left\{\begin{array}{ccc}b=3\\a=5\end{array}\right[/tex]


[tex]Answer:a=5\ and\ b=3\to5x+3y=20.[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.