Algebra
System of Linear Equations
How many solutions are there for this system of equations? \[\begin{align} x + y = 4\\ x + y = 6 \end{align}\]
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?
\[\begin{align} x + 2y &= 4 \\ 3x + 6y &= 12 \end{align}\]