How do you solve x-y=1 ; x+y=3. Please Explain

2 answers:

8 0

You isolate one variable. Let's say that x will be that variable in the first equation:
x-y=1
+y +y
x=y+1
So now you have the equation for x. All you have to do is substitute it into the other:
x=y+1
(y+1)+y=3
Combine like terms and solve:
2y+1=3
-1 -1
2y=2
2y/2=2/2
y=1
Now that you have the value of one, substitute it into either of the equations to find x.
If you put it in the first:
x-1=1
+1 +1
x=2
If you put it into the other, you would get the same answer.
Therefore, y=1 and x=2

zepelin [54]3 years ago

4 0

X - y = 1
x + y = 3
________
2x = 4
__ _
2 2
x = 2
x + y = 3
2 + y = 3
-2 -2
________
y = 1
(x, y) = (2, 1)

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3 years ago

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marin [14]

Option D: $y-7=2(x+1)$ is the equation of line in point - slope form

Explanation:

Given that the slope is $m=2$ and the point $(-1,7)$

We need to determine the equation of the line in point - slope form.

The point - slope form can be determined using the formula,

$y-y_1=m(x-x_1)$

Let us substitute the point $(-1,7)$ and the slope $m=2$ in the above formula.

Thus, we have,

$y-7=2(x-(-1))$

Simplifying the terms, we get,

$y-7=2(x+1)$

Thus, the equation of the line in point - slope form is $y-7=2(x+1)$

Therefore, Option D is the correct answer.

3 0

3 years ago

The point A(-2, 3) is translated using T: (x,y) = (x + 4, y + 2).

Charra [1.4K]

Answer: Choice D) $2\sqrt{5}$

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Work Shown:

Point A starts at (-2,3) and moves to (2,5) after applying the translation rule of "shift 4 to the right, 2 up".

Use the distance formula to find the distance from (-2,3) to (2,5)

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-2)^2 + (3-5)^2}\\\\d = \sqrt{(-4)^2 + (-2)^2}\\\\d = \sqrt{16 + 4}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.472136\\\\$