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Systems of Linear Equations

If one Bitcoin and 100,000 Dogecoin are worth $480, and two Bitcoin and 150,000 Dogecoin are worth $948, would you rather have one Bitcoin or 100,000 Dogecoin?

Systems of Linear Equations Warmup

         

How many solutions are there for this system of equations? \[x + y = 4\] \[x + y = 6\]

Lines \(a, b,\) and \( c\) represent three different linear equations. What is the solution for the system of \(a\) and \(c?\)

Two of these lines intersect at a point with positive coordinates. Which two?

A: \(y = -3x -2\)

B: \(y = 3x -2\)

C: \(y = 0.5x +1\)

D: \(x = -3\)

Find \(xy\) if \(2x + 4y = 2\) and \(y - x = 5\).

How many \((x, y)\) pairs are solutions for both of these equations?

\[\begin{align} x + 2y &= 4 \\ 3x + 6y &= 12 \end{align}\]

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