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

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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 $P_{1} \to (x, y) = (3, 5)$ $P_1->(x,y)=(3,5)$

Explanation:

Given:

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

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

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

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

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

$y = 2 y - 4 - 1$ $y=2y-4-1$

$y = 2 y - 5$ $y=2y-5$

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

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

$0 = y - 5$ $0=y-5$

Add 5 to both sides

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

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

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

$x = 3$ $x=3$

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

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