Answered

IDNLearn.com connects you with a community of experts ready to answer your questions. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

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

Sagot :

Lilithidn
[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 are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.