What ia the sulution of 3y-6x=-3

This is best written as two separate equations:

8x+3y = -23 and 34x+ 5y = -23
Solving the first one for x:
8x = -23-3y
x = -23/8 - 3/8y
Substituting this value for x into the second equation:
34(-23/8 - 3/8y) + 5y = -23
-97.75 - (34)(.375)y + 5y = -23
-97.75 - 12.75y + 5y = -23
-97.75 -7.75y = -23
-7.75y = 97.75-23=74.75
y = -74.75/7.75 = -9.645161
Substitution back into the equation for x:
x = -23/8 - 3/8(-9.645161)
x = -2.875 + 3.616935
x =.741935

The slope is -3 and the y-intercept is -44.

The x intercept is where your line will cross the x axis. Therefore, the value for y at this point is 0. Substitute 0 for y in this equation and solve for x.

6x + 3(0) = 27
x = 27/6
x = 4 1/2

x intercept = (4 1/2, 0)

Follow the same reasoning for the y intercept.

6(0) + 3y = 27
y = 27/3
y = 9

y intercept = (0,9)

Now plot these two points and draw your line through them.

Calcualte the slope of the line as
a=(7-(-11))/(10-(-5))=18/15=6/5
Use the fact that the line passes through one of the two points, for example (10,7)
7=(6/5)*10+b=12+b
Obtain b as b=7-12=-5
The equation of the line in functional form is y=(6/5)x-5
Multiply everything by 5 to clear the fraction
5y=6x-25 or 0=6x-5y-25
Finally, the equation in general form (standard?) is 6x-5y-25=0.

Check the calculation by verifying that the point (10,7) lies on the line.
6(10)-5(7)-25=60-35-25=60-60=0 CHECKed!
Check that the second point (-5,-11) lies on the line also (if you want to)
6*(-5)-5*(-11)-25=-30+55-25=0
That checks OK.

Price of bag of chips s X and price of box of pretzels is Y.
Now you can write following equations:

2X+3Y=413
X+2Y=239

From second equation you know that X is 239-2Y, and you put that in first equation:

2*(239-2Y)+3Y=413

or

-4Y+3Y=413-2*239

Finally we have for Y: Y=65 and X=239-2Y=109.

Select the EQN computational mode 5:EQN

For system of linear equations in 3 unknowns select 2: in the screen below.

Arrange the variables in your equations in the same order (x first, y second, and z third).
The coefficients to enter in the editor are the factors of the variables: In your case a_1=10, b_1=-3, c_1=10, d_1=5, a_2=8, b_2=-2, c_2=9, d_2=3; a_3=8, b_3=1, c_3=-10, d_3=7.
To enter d_1, d_2, and d_3 you will have to scroll to the right to reach the cells where they should go.

Once finished entering the coefficients, press EXE to get the solutions. You may have to use the arrow Down to display the y- and z-solutions.
I verified that the matrix is non-singular and the system has a solution. In fraction form
x=27/53, y=-1 and 22/53; finally z=-23/53

(2x - 3y)(3x + 2y) = 2x*3x + 2x*2y - 3y*3x - 3y*2y
= 6x^2 + 4xy - 9xy - 6y^2
= 6x^2 - 5xy - 6y^2 You multiply each element in the first set of brackets by each element in the second set of brackets and then consolidate like terms and arrange them in sequence of powers, first x and then y. So:
2x by 3x = 6x squared
2x by 2y = 4xy
-3y by 3x = -9xy
-3y by 2y = 6y squared

6x squared -5xy + 6y squared

use the slope-intercept form to graph y=2/3x+4

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

Add the two equations side by side,

2y - x + x = 3 + 3y - 5

2y = 3y - 2

y = 2

Plug this in the second equation to get x,

x = 3(2) - 5

x = 1

So the solution is x = 1, y = 2

or in ordered pair notation (1, 2)