All categories

3 years ago

Solve the equationsY=2x-4, 3x+y=1

Mathematics

1 answer:

liberstina [14]3 years ago

6 0

Step-by-step explanation:

$y = 2x - 4$

$3x + y = 1$

$y = 1 - 3x$

Equating,

$2x - 4 = 1 - 3x$

$2x + 3x = 1 + 4$

$5x = 5$

$x = 1$

Placing it,

$y = 1 - 3( 1)$

$y = 1 - 3$

$y = - 2$

You might be interested in

The ratio of a model scal die cast motorcycle is 1:18. the model is 5.25 inches long. what is the length of the actual motorcycl

Rudik [331]

1: 18 = 5.25/x
18(5.25)=1x
94.5=1x
94.5/1=1x/1
94.5= 7ft 10 1/2 in
PROBABLY WRONG CHECK WITH SOMEONE

4 0

2 years ago

DIscrete Math

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

2 years ago

An average family of 4 creates about 17.6 pounds of garbage every day. About how

Vlad [161]

4.4 is the answer for that problem 17.6 divided by 4

3 0

2 years ago

PLEASEEEEEEEEEEEEEEEE

tatyana61 [14]

Answer:

11.3353

Step-by-step explanation:

please mark me brainliest.

I am begging

6 0

2 years ago

Read 2 more answers

Put the following equation of a line into slope-intercept form, simplifying all

Alexeev081 [22]

Answer: x-3y+21=0

Step-by-step explanation:

move the constant to the left then divide both sides then booom

6 0

2 years ago

Solve the equationsY=2x-4, 3x+y=1​

Solve the equationsY=2x-4, 3x+y=1