How do you solve y=2x-1 and y=x+2?

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Answer 1 · 2016-08-05T08:57:37

First part of the calculation given in detail so that you can see the method more clearly. The second part uses shortcuts.

Point of intersection $P_1->(x,y)=(3,5)$

Given:

$y=2x-1$ ....................Equation(1)
$y=x+2$ .....................Equation(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider equation 2

Subtract $color(blue)(2)$ from both sides

$color(brown)(ycolor(blue)(-2)=x+2color(blue)(-2))$

$y-2=x$ ..........................Equation(3)
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Using equation(3) substitute for $x$ in equation(1)

$y=2(y-2)-1$

$y=2y-4-1$

$y=2y-5$

Subtract $color(blue)(y)$ form both sides

$color(brown)(ycolor(blue)(-y)=2ycolor(blue)(-y)-5)$

$0=y-5$

Add 5 to both sides

$y=5$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute $y=5$ into either equation(1) or (2). I chose (2)

$y=x+2" "->" "5=x+2$

$x=3$

Tony B