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Omni-MATH / Let a,b, and c be real numbers. Consider the system of simultaneous equations in variables x and y: ax+by=c−1 and (a+5)x+(b+3)y=c+1. Determine the value(s) of c in terms of a such …

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problem

Let a,ba, b, and cc be real numbers. Consider the system of simultaneous equations in variables xx and y:y: ax+by=c−1a x+b y =c-1 and (a+5)x+(b+3)y=c+1(a+5) x+(b+3) y =c+1. Determine the value(s) of cc in terms of aa such that the system always has a solution for any aa and bb.
Plain-text mathematical notation (without MathML)
Let a,b, and c be real numbers. Consider the system of simultaneous equations in variables x and y: ax+by=c−1 and (a+5)x+(b+3)y=c+1. Determine the value(s) of c in terms of a such that the system always has a solution for any a and b.
Original LaTeX notation
Let $a, b$, and $c$ be real numbers. Consider the system of simultaneous equations in variables $x$ and $y:$ $a x+b y =c-1$ and $(a+5) x+(b+3) y =c+1$. Determine the value(s) of $c$ in terms of $a$ such that the system always has a solution for any $a$ and $b$.

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Source and history

task_id
de40c769-fe57-5337-a528-8ba320bc93c2
task_key
test--de40c769-fe57-5337-a528-8ba320bc93c2
task_revision_id
1
config / split
/ test

Official source

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