Help please: Solve the system of equations?

Question

-3y+4x= -19
-2y-3x= -24

Best answer chosen tomorrow!

Answer 1

[-3y+4x=-19]-1.5*[-2y-3x=-24]
17x/2=17
x=2
-3y+8=-19
-3y=-27
y=9
(2,9)

Answer 2

Step 1: Multiply Eq. 1 with -2 and Eq. 2 with 3.

-2 . (-3Y + 4X = -19) -------> 6Y - 8X = 38
3 . (-2Y - 3X = -24) -------> -6Y - 9X = -72

Step 2: Add both equations, that should result ----> -17X = -34

Step 3: Divide both sides with -17, would result ----> X = 2

Step 4. Put X = 2 in either equation. If placed into equation 1 ----->
-3Y + 4(2) = -19 -----------> -3Y + 8 = -19

Step 5: Substract 8 from both sides ----> -3Y + 8 -8 = -19 -8
-3Y = -27

Step 6: Dived both sides with -3 ----> Y = 9

Step 7: Check: Place X = 2 and Y = 9 in both equations.

-3(9)+4(2) = -27+8 = -19 Correct
-2(9)-3(2) = -18-6 = -24 Correct

Therefore, the answer X=2 and Y=9 is correct.

I hope that helps.

Answer 3

You get lower common multiples by using the 3 & 2 rather than the 4 & 3. Multiply the top equation by 2 and the bottom equation by (-3) to get

-6y + 8x = -38
6y + 9x = 72

Add these together, eliminating the y:

17x = 34

which gives x = 2. Plug that into your second equation:

-2y - 3(2) = -24

Change signs and divide everything by 2 to get

y + 3 = 12

and y = 9.

Check:

-3(9) + 4(2) = -27 + 8 = -19 OK
-2(9) - 3(2) = -18 -6 = -24 OK

Answer 4

-3y + 4x = -19
-2y - 3x = -24

Multiply the top by -2 and bottom by 3

6y - 8x = 38
-6y - 9x = -72

-17x = -34
x = 2

-3y + 4(2) = -19
-3y + 8 = -19
-3y = -27
y = 9

x = 2
y = 9

Answer 5

x=3y-19/4
Putting the value of x in equation 2
-2y-3(3y-19/4)=-24
-8y-9y+57=-96
17y=153
y=9
Now, x=3y-19/4
x=27-19/4
x=2

Thus, x=2 and y=9

Answer 6

Take the first equation and solve for x in terms of y:

-3y+4x= -19
4x= -19+3y
x= -4.75+0.75y

Then take this expression for x and substitute into the second equation:

-2y-3x=-24 becomes
-2y-3(-4.75+0.75y)=-24

You now have one equation with only y's in it. You can solve for y. And then once you figure out what y equals, you can use the equation x= -4.75+0.75y to solve for x.

Answer 7

Im a big fan of the pseudoinverse method, but I dont know if you like linear algebra. Its fast, powerful, and extensible.

First you make a matrix of the coefficients
A=
[[ -3 4 ]
[-2 -3]]

and a matrix of the results
b=[[-19][-24]]

[y,x]=inv(A'*A)*b

You could also make an augmented matrix and reduce it to reduced row echelon form

B= [A |b]
[y,x]=rref(B(:,3))

or you could solve one equation for one variable, and substitute it into the other, and solve that equation for the remaining variable.

The numbers are very specific here.
Are you asking someone to do your homework?

Answer 8

5x + 2y = 15 -5x - 2y = -5 _____________ 0 = 10 you clean up using combining words, you upload the two equations. 0=10 skill this technique of equation has no answer in any respect, as a results of fact the slopes of the two lines are a similar, in different words are parallel lines, so there isn't any longer factor of interception

Answer 9

-3y+4x= -19
-2y-3x= -24
Convert those equations into :
-6y+8x= -38 (1st equation)
-6y-9x= -72 (2nd equation)
Then subtract : 1st - 2nd
-6y+8x=-38
-
-6y-9x=-72
________________
17x= 34
Hence : x=2
Substitute x into one of the initial equation.
-3y+8= -19
Hence y=9

Answer 10

thts easy
4x-3y=-19...............(1)
-3x-2y=-24..............(2)
multiplying (1)by 3 and (2) by 4
we get
12x-9y= -57
-12x-8y= -96
adding em
we get -17y= -153
as 12x and -12x get cancelled off
from -17y= -153
y=9
putting value of y=9 in (2)

-3x -2(9)= -24
-3x = -6
x = 2

so y = 9 and x = 2