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

Find \( a \) and \( b \).

a x + b y = 20 ( − 2 , 10 ) a ∗ ( − 2 ) + b ∗ 10 = 20 − 2 a + 10 b = 20 ( 1 , 5 ) a ∗ 1 + b ∗ 5 = 20 a + 5 b = 20
{ − 2 a + 10 b = 20 a + 5 b = 20 / ∗ 2 ​ { − 2 a + 10 b = 20 2 a + 10 b = 40 ​ − − − − − − − − 20 b = 60 / : 20 b = 20 60 ​ = 3
− 2 a + 10 b = 20 − 2 a + 10 ∗ 3 = 20 − 2 a + 30 = 20 − 2 a = 20 − 30 − 2 a = − 10 / : ( − 2 )
a = 2 10 ​ = 5 { a = 5 b = 3 ​

Answered by Lilith | 2024-06-10

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 +\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
A n s w er : a = 5 an d b = 3 → 5 x + 3 y = 20.

Answered by Anonymous | 2024-06-10

The values of a and b are found to be a = 5 and b = 3 from substituting the points into the given line equation. This results in a system of equations that can be solved step-by-step. By isolating variables and substituting, we determined the values accurately.
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Answered by Lilith | 2024-12-23