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# Linear Equations

Your music collection grows by 20 songs every week. If you currently have 1,000 songs, how many weeks will it take to amass 3,500 songs?

# 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.

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 $$a+b$$?

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