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

Aug 5, 2016

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 ${P}_{1} \to \left(x , y\right) = \left(3 , 5\right)$

Explanation:

Given:

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

Subtract $\textcolor{b l u e}{2}$ from both sides

$\textcolor{b r o w n}{y \textcolor{b l u e}{- 2} = x + 2 \textcolor{b l u e}{- 2}}$

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

$y = 2 \left(y - 2\right) - 1$

$y = 2 y - 4 - 1$

$y = 2 y - 5$

Subtract $\textcolor{b l u e}{y}$ form both sides

$\textcolor{b r o w n}{y \textcolor{b l u e}{- y} = 2 y \textcolor{b l u e}{- y} - 5}$

$0 = y - 5$

Add 5 to both sides

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

$y = x + 2 \text{ "->" } 5 = x + 2$

$x = 3$ 