How do you solve $x = 2 y - 2$ $x = 2y - 2$ and $3 x - y = 14$ $3x - y = 14$ using substitution?

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How do you solve $x = 2 y - 2$ $x = 2y - 2$ and $3 x - y = 14$ $3x - y = 14$ using substitution?

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Answer 1 · 2018-04-27T17:52:46

$(x, y) \to (6, 4)$ $(x,y)to(6,4)$

Explanation:

$x = 2 y - 2 \to (1)$ $x=2y-2to(1)$

$3 x - y = 14 \to (2)$ $3x-y=14to(2)$

$equation (1) expresses x in terms of y$ $"equation "(1)" expresses x in terms of y"$

$Substitute x = 2 y - 2 into equation (2)$ $color(blue)"Substitute "x=2y-2" into equation "(2)$

$\Rightarrow 3 (2 y - 2) - y = 14$ $rArr3(2y-2)-y=14$

$\Rightarrow 6 y - 6 - y = 14$ $rArr6y-6-y=14$

$\Rightarrow 5 y - 6 = 14$ $rArr5y-6=14$

$add 6 to both sides$ $"add "6" to both sides"$

$\Rightarrow 5 y = 20 \Rightarrow y = \frac{20}{5} = 4$ $rArr5y=20rArry=20/5=4$

$substitute y = 4 into equation (1)$ $"substitute "y=4" into equation "(1)$

$\Rightarrow x = (2 \times 4) - 2 = 6$ $rArrx=(2xx4)-2=6$

$the point of intersection of the 2 equations = (6, 4)$ $"the point of intersection of the 2 equations "=(6,4)$
graph{(y-1/2x-1)(y-3x+14)((x-6)^2+(y-4)^2-0.04)=0 [-10, 10, -5, 5]}

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How do you solve $x = 2 y - 2$ $x = 2y - 2$ and $3 x - y = 14$ $3x - y = 14$ using substitution?

1 Answer

Explanation:

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How do you solve $x = 2 y - 2$ $x = 2y - 2$ and $3 x - y = 14$ $3x - y = 14$ using substitution?