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creativ13 [48]
4 years ago
6

How can I tell if a system of equations has one, no, or infinitely many solutions?

Mathematics
1 answer:
Fittoniya [83]3 years ago
7 0

Answer:

There are many ways to interpret if whether or not a system of equations has solutions or not. Here is one way that is most ideal for most, if not, all equations: using graphs.

  • If the graphs of the set of equations do NOT intersect, then there are no solutions (because no x or y value will ever make both equations true)
  • If the graphs of the set of equations DO intersect at one point, then ONLY that one point will make both equations true. (One solution)
  • If the graphs of the set of equations are identical on the graph, then there are infinite solutions that make both equations true.

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Two friends share £150 in the ratio 4:11<br> (a) How much does each friend receive?
aliya0001 [1]

Step-by-step explanation:

Total ratio=4+11

=15

1st friend's share

= 4/15 x 150

=4 x 10

=£40

2nd friend's share

=11/15 x 150

=11 x 10

=£110

5 0
3 years ago
Evaluate the expressions 3x-2 and 4x+4 for the following value of x.
kirill [66]

Question:

Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2

Answer:

Part a: 4x+4>3x-2

Part b: 4x+4=3x-2

Part c: 4x+4>3x-2

Part d: 4x+4>3x-2

Explanation:

Part a: Substituting x=0, we get,

\begin{aligned}3 x-2 &=3(0)-2 \\&=-2\end{aligned}

\begin{aligned}4 x+4 &=4(0)+4 \\&=4\end{aligned}

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Part b: Substituting x=-6, we get,

\begin{aligned}3 x-2 &=3(-6)-2 \\&=-18-2 \\&=-20\end{aligned}

\begin{aligned}4 x+4 &=4(-6)+4 \\&=-24+4 \\&=-20\end{aligned}

The value of 3x-2 and 4x+4 are equal.

Thus, 4x+4=3x-2

Part c: Substituting x=5, we get,

\begin{aligned}3 x-2 &=3(5)-2 \\&=15-2 \\&=13\end{aligned}

\begin{aligned}4 x+4 &=4(5)+4 \\&=20+4 \\&=24\end{aligned}

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Part d: Substituting x=-2, we get,

\begin{aligned}3 x-2 &=3(-2)-2 \\&=-6-2 \\&=-8\end{aligned}

\begin{aligned}4 x+4 &=4(-2)+4 \\&=-8+4 \\&=-4\end{aligned}

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

4 0
3 years ago
Hurry please!! Write an equation of the line in slope-intercept form
juin [17]

Answer:

D

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
PLEASE HELP ME WITH THIS I NEED HELP
jasenka [17]

Answer:

a. y = -x

b. Area = xy

c. x = -y

Step-by-step explanation:

a. The perimeter of the garden is the distance all the way around, in this would be x+y+x+y, or 2x + 2y. To solve for y, we’re trying to isolate it on one side. We need to subtract 2x to get 2y = -2x. Divide by 2 to get y = -x.

b. Area is length times width, so x • y, or xy.

c. To express in terms of x, we can take the equation y = -x and multiply it by -1 to get x = -y

3 0
2 years ago
If your playing a game and get 15 coins 30 minutes. How many coins will you get in 1 hour and 40 minutes?
Arisa [49]

Answer:

You would get 50 coins in that time.

Step-by-step explanation:

To find this, we first need to find the unit rate. We can get that by dividing the amount of coins by the amount of time.

15 coins/ 30 mins = .5 coins per minute.

Now, we have 100 minutes in the second part of the problem, so we multiply the rate by that amount of time.

.5 coins per min * 100 mins = 50 coins

8 0
3 years ago
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