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Linear Equations

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Linear Equations - Intersection of Lines

         

\[ \] In the graph above, \( l_1 \) is a horizontal line with \( y\)-intersept \( 3\), and \( l_2 \) has a slope of \(2\) with \(y\)-intercept \(-1\). Find the coordinates of the intersection point of the two lines.

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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?

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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 \(a\)?

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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 \( a \)?

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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 \(a+b\)?

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