All categories

1 year ago

How many solutions does each system have?

Mathematics

1 answer:

dezoksy [38]1 year ago

6 0

Answer:

System 1 has an infinite number of solutions and System 11 has no solution.

Step-by-step explanation:

System 1:

x = y - 3

x - y = -3

2x - 2y = -6

Divide above by 2:

x - y = -3

So the 2 equations are identical

and they have an infinite number of solutions.

System 11:

5x + 2y = -7

15x + 6y = 21

Divide the above by 3:

5x + 2y = 7

Comparing this to the first equation the left sides are the same but right sides are different ( -7 and 7)/

There is no solution to this system.

You might be interested in

An airplane travels 6111 kilometers against the wind in 9 hours and 7911 kilometers with the wind in the same amount of time. Wh

natima [27]

Answer:

Speed of the plane in still air: $779\; {\rm km \cdot h^{-1}}$ .

Windspeed: $100\; {\rm km \cdot h^{-1}}$ .

Step-by-step explanation:

Assume that $x\; {\rm km \cdot h^{-1}}$ is the speed of the plane in still air, and that $y\; {\rm km \cdot h^{-1}}$ is the speed of the wind.

When the plane is travelling against wind, the ground speed of this plane (speed of the plane relative to the ground) would be $(x - y)\; {\rm km \cdot h^{-1}}$ .
When this plane is travelling in the same direction as the wind, the ground speed of this plane would be $(x + y)\; {\rm km \cdot h^{-1}}$ .

The question states that when going against the wind ( $v = (x - y)\; {\rm km \cdot h^{-1}}$ ,) the plane travels $6111\; {\rm km}$ in $9\; {\rm h}$ . Hence, $9\, (x - y) = 6111$ .

Similarly, since the plane travels $7911\; {\rm km}$ in $9\; {\rm h}$ when travelling in the same direction as the wind ( $v = (x + y)\; {\rm km \cdot h^{-1}}$ ,) $9\, (x + y) = 7911$ .

Add the two equations to eliminate $y$ . Subtract the second equation from the first to eliminate $x$ . Solve this system of equations for $x$ and $y$ : $x = 779$ and $y = 100$ .

Hence, the speed of this plane in still air would be $779\; {\rm km \cdot h^{-1}}$ , whereas the speed of the wind would be $100\; {\rm km \cdot h^{-1}}$ .

3 0

1 year ago

Nelda baked two kinds of pasta in pans. Each pan was the same size she sliced one pan of pasta into 4 equal pieces. She sliced t

Lemur [1.5K]

Answer:

Step-by-step explanation:

I found this be adding 4 and 6, witch is 2.

6 0

3 years ago

Read 2 more answers

SUPER EASY FOR POINTS!!!!solve: x-3=3x-2

Savatey [412]

Answer:

Polynomial equation solver

x-3=3x-2

Standard form:

−2x − 1 = 0

Factorization:

−(2x + 1) = 0

Solutions:

x = −1

= -0.5

3 0

3 years ago

Write a equation for the line parallel to

Llana [10]

Paralell has same slope
y=mx+b
m=slope
b=yint

same slope so other equation is
y=4x+b

input given point
(2,0)
x=2
y=0
0=4(2)+b
0=8+b
minus 8 both sides
-8=b

the equation is y=4x-8

8 0

3 years ago

Simplify the following: (r+s-t)-(r-s+t)

ArbitrLikvidat [17]

R+s-t-(r-s+t)

=2s-t is the answer

People think this answer would be just =2s but I have verified with an online calculator and the answer that textbooks look for regarding this is 2s-t

You would assume you would go r-r and thats 0 so no r's

you would say s-(-s) makes it plus and theres 2s

and you would say -t -(+t) is -t

that's why the answer is 2s-t

At first I also did t-(+t) and thought it would be no t's but the answer is in fact 2s-t

4 0

3 years ago