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Katena32 [7]
3 years ago
11

Solve the following system of equations by substitution: 5x + 2y = 14 y = x – 7 Question 11 options: (–3, 4) (2, –5) (4, –3) (–5

, 2)
Mathematics
1 answer:
goblinko [34]3 years ago
8 0
To solve this system using substitution, start by writing them next to each other. You can see that the y value is already isolated with its own value (x - 7).

So, since y equals that expression, you can substitute it into your first given equation for the y.
This leaves you with:
5x + 2(x - 7) = 14

Then, use the distributive property to simplify your equation.
This ends up with:
5x + 2x - 14 = 14

Combine like terms by adding the coefficients in front of your x’s.
This results in:
7x - 14 = 14

Begin to isolate your variable by adding 14 to both sides.
This leaves you with:
7x = 28

Divide both sides by 7 to find the value of x in your solution.
This results in:
X = 4
So you know that the x value in your final ordered pair will be a 4.
At his point you could eliminate answer options and find the correct one, however to find your y value:

Substitute in your x to the simplest equation you were given in the system at the beginning.
This would be y = x - 7
Plugging in the value leaves you with:
y = 4 - 7
Subtract to find your final answer.
4-7= -3

So your y value is -3.

This makes your final ordered pair option C. (4, -3)
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Find the equation of the circle with a diameter whose end points are (-1,-2) and (-3,2)
Sergeeva-Olga [200]

Answer:

The equation of the circle with a diameter whose end points are (-1,-2) and (-3,2) is

x^{2} +y^{2}+4x-1=0

Step-by-step explanation:

<u>Explanation:</u>-

<u>Step 1:</u>-

The equation of the circle having center and radius is

(x-h)^2+(y-k)^2=r^2

here center is (h,k) and radius is r

Given diameter whose end points are (-1,-2) and (-3,2)

The diameter of the circle is passing through the center of the circle

so center of the circle = midpoint of two end points

      (\frac{-1 +(-3) }{2} ,\frac{-2+2 }{2}  )

    (-2,0)

therefore center (h,k) = (-2,0)

<u>Step 2:-</u>

we have to find the radius of the circle

the radius of the circle = the distance from center to the one end point

i.e., C P = r

Given one end point is P(-3,2) and center C(-2,0)

The distance formula of two points are

\sqrt{(x_{2}-x_{1} ) ^{2}+ (y_{2}-y_{1} ) ^{2}}

r=\sqrt{{(-3)-(-1) ) ^{2}+ (2-(-2)) ^{2}}

r=\sqrt{5}

<u>Step 3</u>:-

center (h,k) = (-2,0) and

radius r=\sqrt{5}

The standard form of circle equation

(x-h)^2+(y-k)^2=r^2

(x-(-2))^2+(y-0)^2=\sqrt{5} ^2

on simplification is

x^{2} +y^{2}+4 x-1=0

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