How do you solve $3 x - 2 y = 2$ $3x-2y=2$ and $- 2 x + y = 8$ $-2x+y=8$ using substitution?

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How do you solve $3 x - 2 y = 2$ $3x-2y=2$ and $- 2 x + y = 8$ $-2x+y=8$ using substitution?

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Answer 1 · 2017-08-21T10:18:55

$(x, y) \to (- 18, - 28)$ $(x,y)to(-18,-28)$

Explanation:

$3 x - 2 y = 2 \to (1)$ $3x-2color(red)(y)=2to(1)$

$- 2 x + y = 8 \to (2)$ $-2x+color(red)(y)=8to(2)$

$from (2) x y = 8 + 2 x \to (3)$ $"from "(2)color(white)(x)color(red)(y)=8+2xto(3)$

$substitute y = 8 + 2 x in (1)$ $"substitute "y=8+2x" in "(1)$

$\Rightarrow 3 x - 2 (8 + 2 x) = 2$ $rArr3x-2(8+2x)=2$

$\Rightarrow 3 x - 16 - 4 x = 2$ $rArr3x-16-4x=2$

$\Rightarrow - x = 18 \Rightarrow x = - 18$ $rArr-x=18rArrx=-18$

$substitute this value in (3)$ $"substitute this value in "(3)$

$\Rightarrow y = 8 + (2 \times - 18) = 8 - 36 = - 28$ $rArry=8+(2xx-18)=8-36=-28$

$As a check$ $color(blue)"As a check"$

$Substitute these values in (1)$ $"Substitute these values in "(1)$

$(3 \times - 18) - (2 \times - 28) = - 54 + 56 = 2 \leftarrow True$ $(3xx-18)-(2xx-28)=-54+56=2larr" True"$

$\Rightarrow point of intersection = (- 18, - 28)$ $rArr" point of intersection "=(-18,-28)$

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How do you solve $3 x - 2 y = 2$ $3x-2y=2$ and $- 2 x + y = 8$ $-2x+y=8$ using substitution?

1 Answer

Explanation:

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How do you solve $3 x - 2 y = 2$ $3x-2y=2$ and $- 2 x + y = 8$ $-2x+y=8$ using substitution?