   SEARCH HOME Math Central Quandaries & Queries  Question from Kieran, a student: Can you help me with this q? Thanks Find the point of intersection of the straight lines y=2x+4 and y+2x-16=0 We have two responses for you

Kieran,

Add -2x + 16 to both sides of the second equation to obtain y = -2x + 16. Thus the two equations you have are

y = 2x + 4
y = -2x + 16

Suppose you have a point that is on both lines and its first coordinate is x. Since it is on the first line its second coordinate y can be found using the expression y = 2x + 4. Since it is on the second equation its second coordinate y can also be found using the expression is -2x + 16. Thus

2x + 4 = -2x + 16

Solve for x.

Penny

Remember that the line y=2x+4 is the set of points (x,y)
for which y does equal 2x+4, and the line y+2x-16=0 id the set of points for which that equation holds.

Thus the intersection is the point (x,y) where both equations hold. At that point it is valid to substitute (2x+4) for y
in the second equation, getting an equation with only "x" that you can simplify and solve.

Good Hunting!
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