Linear Equations
What is the interval of all possible values of \(a\) such that the two lines \(x+y=\lvert a \rvert\) and \(ax-y=196\) intersect in the first quadrant?
Consider the line passing through two points \((5, 0)\) and \((0, -5)\). Consider another line passing through two points \((-4, 0)\) and \((0, -2)\). If these two lines and a third line \(y=ax-85\) intersect at one point, what is the value of the constant \(a\)?
A line passing through the intersection point of the two lines \[ x+2y+3=0\;\;\text{and}\;\; 2x-y+\frac{a}{2}=0 \] also passes through two other points \( (9,\ -8)\ \) and \(\ (-17,\ 9) \). What is the value of \( a \)?
Suppose the intersection point of the two lines \[x-2y-9=0, 2x+3y-53=0\]
is \(P=(a,b)\). What is the value of \(a+b\)?