If given A,B,C, Find constants x,y |xA +yB=C

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To solve for constants x and y in the equation xA + yB = C, where A = 2i + 3j, B = 1i + 5j, and C = -1i + 3j, the approach involves separating the vector equation into its i and j components. This results in two distinct equations that can be solved simultaneously. The initial thought of relating the equation to the slope form was deemed unhelpful. The focus should remain on solving the component equations directly. The discussion emphasizes the importance of breaking down the vector equation for clarity in finding the constants.
astroman707
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Homework Statement


Three vectors are given:
A=2i+3j, B=1i+5j, C=-1i+3j
Find constants x and y such that xA+yB=C

Homework Equations


N/A

The Attempt at a Solution


The form of the final equation reminded me if standard form of a slope, so I found the total vector for A,B, and C. I was then going to put it in the form Ax+By=C, but then I realized I’d be solving for slope, and I don’t think that’s the direction I want to go.
 
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try separating the vector equation xA + yB into their two components - that is two equations, one for i and one for j
 

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