How do you solve x – y = 3 and 2x + 2y = 2?

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How do you solve x – y = 3 and 2x + 2y = 2?

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Answer 1 · 2018-06-14T11:09:12

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

Explanation:

From the first equation, $x = y + 3$ $x=y+3$ . Substitute in to the second:
$2 (y + 3) + 2 y = 2$ $2(y+3)+2y=2$ . Multiply this out: $2 y + 6 + 2 y = 2$ $2y+6+2y=2$ . Collect terms: $4 y = - 4$ $4y=-4$ , so $y = - 1$ $y=-1$ .

Return to the first equation: $x - (- 1) = 3$ $x-(-1)=3$ , so $x = 2$ $x=2$ .

Answer 2 · 2018-06-14T11:09:55

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

Explanation:

$x - y = 3 \to (1)$ $x-y=3to(1)$

$2 x + 2 y = 2 \to (2)$ $2x+2y=2to(2)$

$from equation (1) \to x = 3 + y \to (3)$ $"from equation "(1)tox=3+yto(3)$

$substitute x = 3 + y into equation (2)$ $"substitute "x=3+y" into equation "(2)$

$2 (3 + y) + 2 y = 2$ $2(3+y)+2y=2$

$6 + 2 y + 2 y = 2$ $6+2y+2y=2$

$subtract 6 from both sides$ $"subtract 6 from both sides"$

$4 y = - 4 \Rightarrow y = \frac{- 4}{4} = - 1$ $4y=-4rArry=(-4)/4=-1$

$substitute y = - 1 into equation (3)$ $"substitute "y=-1" into equation "(3)$

$x = 3 - 1 = 2$ $x=3-1=2$

$point of intersection = (2, - 1)$ $"point of intersection "=(2,-1)$
graph{(y-x+3)(y+x-1)=0 [-10, 10, -5, 5]}

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How do you solve x – y = 3 and 2x + 2y = 2?

2 Answers

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