Solve the following system of equations using any method you want. 10y+24=-3x 3x-9=y

Please help ASAP IM IN DESPREATE NEED OF HELP

Advocard [28]

Answer:

See the attached image for the graph of the first system.

Step-by-step explanation:

Here's how to graph the first system.

Start with the inequality $-y \le -2x-3$ . You can make this easier to work with by multiplying through by -1. Remember to switch the inequality sign when multiplying by a negative number. OK, you get the inequality

$y \ge 2x+3$ .

The graph will be a half-plane -- all the points on one side of a line. The line that is the boundary of the half-plane has an equation: $y=2x+3$ -- just use an = sign instead of the inequality sign.

Graph the line.

The equation of the line is in slope-intercept form: y = mx + b, so you can tell the y-intercept is 3 and the slope is 2 (think of it as a fraction 2/1). Graph the line by going to the point (0, 3) -- the y-intercept -- then use the slope 2/1 interpreted as "rise over run" to go up 2 units and right 1 unit, arriving at the point (1, 5). Draw the line through those points, (0, 3) and (1, 5).

Now you have to decide which side of the line the inequality $y \ge 2x+3$ is describing. To do this, pick a point which is not on the line, plug its coordinates into the inequality; if the result is true, shade the side of the line the point you picked is on (if false, shade the other side!)

An easy point to pick in this case is the origin, (0, 0). Put zeros in for x and y in the inequality, and you'll get the statement $0 \ge 2(0)+3 \, \Rightarrow \, 0 \ge 3$ . That's false, so shade the side of the line not containing the origin. In the image below, the shading is in purple.

All right, now for the other inequality, $x+2\le 0$ . Subtract 2 from both sides and the inequality becomes $x \le -2$ . This, too, graphs as a half-plane whose boundary line has equation $x=-2$ . Graph the line. A line with an equation that has x in it but not y is a vertical line with all its x-coordinates equal to the number on the right side of the equation. This line is vertical and goes through points such as (-2, 0).

Pick a point not on the line (the origin works again). Put the coordinates into the inequality to get $0\le -2$ which is false. Shade the side of the vertical line which does not contain the origin. In the image below, the shading is in black.

Finally, YAY! \o/ , the solutions to the system are all the points in the plane that got shaded twice. In the image, they are the cross-hatched points above the purple line and to left of the black line.

Note: If you get a system with three inequalities, you'll be graphing three half-planes and looking for points that got shaded three times!

Note: One of your questions has the inequalities $x \ge 0$ and $y \ge 0$ in it. These two inequalities say that the x and y coordinates are both positive or zero, confining your attention to Quadrant I in the upper-right part of a graph, above the x-axis and to the right of the y-axis.

7 0

3 years ago

How many pints are there in 6 quarts 1 pint

yawa3891 [41]

Answer:

There are 13 pints in 6 quarts and 1 pint.

8 0

3 years ago

Read 2 more answers

Solve the equation identify extraneous solutions

PIT_PIT [208]

Answer:

Step-by-step explanation:

The goal to solving any equation is to have x = {something}. That means we need to get the x out from underneath that radical. It's a square root, so we can "undo" it by squaring. Square both sides because this is an equation. Squaring both sides gives you

$x^2=-3x+40$

Get everything on one side of the equals sign and set the quadratic equal to 0:

$x^2+3x-40=0$

Throw this into the quadratic formula to get that the solutions are x = 5 and -8. We need to see if only one works, both work, or neither work in the original equation.

Does $5=\sqrt{-3(5)+40}$ ?

$5=\sqrt{-15+40}$ and

$5=\sqrt{25}$

and 5 = 5. So 5 works. Let's try -8 now:

$-8=\sqrt{-3(-8)+40}$ and

$-8=\sqrt{24+40}$ so

$-8=\sqrt{64}$

-8 = 8? No it doesn't. So only 5 works. Your choice is the third one down.

6 0

3 years ago

This looks pretty easy but i have no idea how you do it can someone help? thanks :)

DochEvi [55]

Answer:

BOI YOU TALKING ABOUT SOME THIS LOOKS EASY, THIS DOESN'T EVEN LOOK EASY PLUS... i dont know the answer. Bye

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Select the correct answer. Consider the following system of equations. Use this graph of the system to approximate its solution.

vesna_86 [32]

The approximate solution to the given system of equations, considering the graph, is given as follows:

D. $\left(-\frac{13}{4}, \frac{5}{2}\right)$ .

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:

D. $\left(-\frac{13}{4}, \frac{5}{2}\right)$

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

7 0

2 years ago