How Can You Solve for A and B Using Points (4,1) and (-5,-3)?

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To solve for integers A and B using the points (4,1) and (-5,-3) in the equation Ax + By = 7, two equations are derived: 4A + B = 7 and -5A - 3B = 7. These equations can be solved using methods such as substitution or elimination. The suggestion to use a matrix and row reduction is also mentioned as a viable approach. The discussion emphasizes that with two equations and two unknowns, the problem is straightforward. Understanding the concepts from a linear algebra textbook can aid in finding the solution.
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Find integers A and B such that (4,1) and (-5,-3) are solitions to Ax + By = 7
 
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Plug them into x and y to get:

4A + B = 7

and

-5A + -3B = 7

And solve :smile:
 
try putting the coefficients and answers into a matrix and Row reduce...

oh... sorry, just finished a semester in Linear Algebra :-)

but really... you have 2 equations that are equal to each other ad 2 unknowns... that is easy to solve just read the math book you have (I know, I know who reads a math book :-D )
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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