What is the solution of this system?? Thanks tons!?

Subtract the equations

4x - y = 17
4x + 5y = -13
---------------------------
0 - 6y = 30

or y = -5

put y = -5 in first equation

4x -(-5) = 17
=> 4x = 17 - 5
=> x = 3

in an ordered pair form,

(x,y) = (3, -5)

4x - y = 17 (solve by using substitution)
4x + 5y = -13

4x - y = 17
4x = y + 17

4x + 5y = -13
(y + 17) + 5y = -13
y + 17 + 5y = -13
y + 5y = -13 - 17
6y = -30
y = -30/6
y = -5

4x - y = 17
4x - (-5) = 17
4x + 5 = 17
4x = 17 - 5
4x = 12
x = 12/4
x = 3

∴ x = 3 , y = -5

You can either add the two equations together or use substitution to solve the equation. Substitution is too messy for this so we'll add.

You want one of the variables to cancel out. Multiply one of the equations by -1 to get rid of the x.

4x + 5y = -13
4x - y = 17 (Multiply by -1.)

4x + 5y = -13
-4x + y = -17
---------------------- (Now add.)
6y = -30 (Solve for y.)
y = -5

Now that you have y, plug it into one of the original equations to find x.

4x - y = 17
4x - (-5) = 17
4x + 5 = 17
4x = 12
x = 3

Now use x and y to write an ordered pair.

(3,-5)

To check your work, plug the values into the second original equation.

4x + 5y = -13
4(3) + 5(-5)
12 + (-25) = -13

(3,-5)
It is the only solution, as both x and y are in the first power.

4x - y = 17 implies that y = 4x -17. So, by the 2nd equation

4x + 5(4x - 17) = -13
4x + 20 x - 85 = -13
24x = 72
x=3

In the first Eq
4x3 - y = 17
12-y=17
y=-5

(3,-5)

4x - y = 17 Eq (1)
4x+ 5y = -13 Eq (2)

20x - 5y = 85 Eq (1) x 5
4x + 5y = -13 Eq (2)
----add------
24x = 72
x = 3

4x+ 5y = -13 Eq (2)
4x - y = 17 Eq (1)
----subtract---
6y = -30
y = -5

(x, y) = (3, -5)

Subtract equation (2) from equation (1)
-6y =30
y=-5
Substitute this y into equation (1)
4x-(-5) =17
4x+5=17
4x=12
x=3
x=3, y=-5
(3,-5) is the solution

4x-y=17....(1)
4x+5y=-13...(2)
.-.....-.......+........
-6y=30
y=5 added to ..(1)
4x-y=17
4x-5=17
4x=17+5
4x=22
x=11/2