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4 years ago

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:

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