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Elena L [17]
2 years ago
11

How many solutions does the system have?

Mathematics
1 answer:
bearhunter [10]2 years ago
6 0

Answer:

A. Exactly one solution

Step-by-step explanation:

Solve the system of equations.

y = x + 1

y = 2x - 5

Substitute one equation into the other.

y = 2x - 5

x + 1 = 2x - 5

Subtract 2x from both sides.

-x + 1 = -5

Subtract 1 from both sides.

-x = -6

Multiply both sides by -1.

x = 6

Put it back into the other equation.

y = x + 1

y = 6 + 1

Add.

y = 7

The solution is (6, 7). Since the equations aren't equal, there are not infinitely many solutions, but since there is a solution found, we can determine that there is exactly one solution.

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The edges of the diameter of a circle are at (-1,2) and (3,-1). Write the equation of the circle in general form.
Y_Kistochka [10]

Answer:

(x-1)²+ (y-0.5)²=6.25

Step-by-step explanation:

<u>The standard form of equation of a circle is;</u>

(x-a)²+(y-b)²=r² where (a,b) are the center of the circle and r is the radius

<u>Finding the mid-point of the given points</u>

(-1,2) and (3,-1)⇒midpoint will be 1/2(x₁+x₂) , 1/2(y₁+y₂)

midpoint= {1/2(-1+3), 1/2(2+-1)}

midpoint=(1,0.5)

<u>Finding the radius r; the distance from the center to either of the given two points</u>

Apply the distance formula d=√ (x₂-x₁)² +(y₂-y₁)²

Taking (x₁,y₁) as (1,0.5) and (x₂,y₂) as (-1,2) then

d=√ (-1-1)² +(2-0.5)²

d= √ (-2)²+(1.5)²

d=√4+2.25⇒√6.25⇒2.5

r=2.5

<u>Equation of the circle</u>

(x-1)² + (y-0.5)²=2.5²

(x-1)²+ (y-0.5)²=6.25

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Answer:

1 hour

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dividing LHS and RHS by 1.5 so that we get 1 hour in LHS

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