Pre-Calculus. PLEASE Help. Best answer 10 points.?

Question

I don't understand what it's asking me to do.

Solve the system graphically.
x + y = 0
3x - 2y = 10

and

-x + 2y = 1
x - y = 2

Can someone explain to me how to do it.
If you find it necessary, show me the work as well?
Thanks. I appreciate it.
No rude comments. I look down upon those!
Muchos Gracias.

Answer 1

It's asking you to draw the line of each equation. Where the two lines intersect is the answer.

Using algebra on the first problem
x+y=0 So, y=-x
3x-2y=10
3x -2(-x) = 5x = 10
x=2; y = -2
Graphically the lines intersect at (2,-2)

Second
-x+2y=1 So, x = 2y-1
x-y=2
(2y-1)-y=2
y-1 = 2
y=3; x=5
Graphically, the two lines intersect at (5,3)

Answer 2

First, it's muchas gracias not muchos gracias. Second, the problems are asking you to find where the two equations intersect or cross each other on the cartesian coordinate plane.

To graph these you will can rewrite them in slope intercept form (y=mx +b) or you can solve for the intercepts and graph them that way (my favorite method). For each equation, just plug in zero for y and solve for the x-intercept and then plug in 0 for x and solve for the y-intercept. You only need two points to plot a line and then you can approximate (to the nearest tenth hopefully) what the coordinates of their crossing point (the intersection) are.

So to recap:
Step 1: Find the x and y intercepts of each equation in a system and plot these line that goes through each pair of intecepts.
Step 2: Locate the point where the two lines cross each other on your graph. This coordinate pair is called the solution.

Here's how to do Step 1 for the first system:

Equation 1:
x + y = 0 so y = - x => (0,0) and (1,-1) are points on this line. Plot them and draw a line right through.

Equation 2:
3x-2y=10 so let's solve for the x and y intercepts
x-intercept: 3x - 2(0) = 10 so 3x = 10 and x = 10/3
thus the x-intercept is (3 1/3, 0)
y-intercept: 3(0) - 2y = 10 so -2y = 10 and y = 10/-2
thus the y-intercept is (0, -5)
Plot a line through (3 1/3, 0) and (0, -5) and then find where these two lines intersect each other. This point of intersection is the solution of the system of equations.

Answer 3

okay first solve both equations for y to get the following:

y = -x
y = 3/2x -5

Now since they want you to do this graphically you're looking for when these two lines intersect. So lets take the first equation. Plug 0,1,2,3 in for x and then see what your (y) becomes. For example. If i plug 2 in for x, y becomes -2. So that point is (2,-2). Do the same for 1, 2, and 3 to get three points then plot them and draw that line.

For the second equation i would plug in 0, 2, and 4 in for x.
You'll get these point when you do respectively.
(0,-5) (2,-2), and (4,1). Plot those points and draw the line for that equation. You'll notice that they intersect at (2,-2). Therefore the system of equations is ture when x = 2 and y = -2.

You should be able to do the second on your own just following the same steps

Answer 4

For the first one, there is no need to solve it graphically.
X + y =0 and 3x - 2y=10
first x+ y = 0, rearrange and x = y.

Plug x=y into 2nd equation and you get 3y - 2y = 10 so y= 10.

*******
for
-x + 2y = 1 (A)
x - y = 2 (B)

Add equations (A) and (B)
(A) + (B) cancels the x's. y=3. Plug y=3 into equation (B)
x - 3= 2, x=5, y=3

Answer 5

To solve the problem you have to graph both of them on a calculator and then trace and find the point or points of intersection

(you can't directly put them in the caluculator because the y has to be by itself so solve for y:
x+y=0 subtract x from both sides
y=x

3x-2y=10; subtract 3x and then divide by -2
y=(-3x+10)/-2

plug both in and find the point of intersection)

(if using a ti graphing calculator to find point of intersection you can press 2nd then trace and then press intercept. pick one point on the left and another point on the right and then press enter again and they will tell you the point of intersection. You want the x point.)

Answer 6

Put the two equations on a graph and see where they meet. You are looking for their intercept.

Answer 7

so the perimeter is 8. 8=2x+2y 8-2y=2x 4-y=x. if the length is x so is the height. 1/2*x^2=A.