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miskamm [114]
3 years ago
6

Two solutions of the equation Ax+By = 1 are (2, -1) and (-3,-2). Find A and B.

Mathematics
1 answer:
kati45 [8]3 years ago
4 0

Answer:

Substitute in the values of both given coordinates & form 2 equations:

\left \{ {{A(2)+B(-1)=1} \atop {A(-3)+B(-2)=1}} \right. \\\\=\left \{ {{2A-B=1} \atop {-3A-2B=1}} \right.

Find the value of B from the equation 2A - B = 1:

2A-B=1\\-B=1-2A\\B=2A-1

Substitute in the B-value to the other equation:

-3A-2B=1\\-3A-2(2A-1)=1\\-3A-4A+2=1\\-7A=1-2\\-7A=-1\\A=\frac{-1}{-7} =\frac{1}{7}

Find the B-value using the equation from before:

B=2A-1=2(\frac{1}{7})-1=\frac{2}{7} -\frac{7}{7} =-\frac{5}{7}  

Therefore the equation Ax + By = 1 would equal:

\frac{1}{7} x-\frac{5}{7} y=1

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