Write as a Vector Equality 5a+3b=35 , a/b=2/5

Problem

5*a+3*b=35,a/b=2/5

Solution

1. Rearrange the second equation to eliminate the fraction by cross-multiplying.

5*a=2*b

2. Rewrite the equation 5*a=2*b in standard form by moving all variables to one side.

5*a−2*b=0

3. Identify the system of linear equations formed by the two expressions.

5*a+3*b=35

5*a−2*b=0

4. Express the system as a vector equality by separating the coefficients of a and b into column vectors.

a*[[5],[5]]+b*[[3],[−2]]=[[35],[0]]

Final Answer

a*[[5],[5]]+b*[[3],[−2]]=[[35],[0]]

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