7x+2y=17 5x+6y=3?

the second equation minus 3 times the first equation give you:

-16x = -48 so x = 3 and then 7*3 + 2y = 17 so 2y = -4 so y=-2

7x+2y=17----(1)
5x+6y=3 -----(2)
2y = 17-7x
y=6.5-3.5x---(3)
5x + 6(6.5 - 3.5x) = 3
5x + 39 - 21x = 3
-16x + 39 = 3
-16x = -36
x =2.25
7(2.25)+2y = 17
15.75 + 2y = 17
2y=1.25
y=0.625

x=2.25 , y=0.625
_____________

- 21x - 6y = - 51
5x + 6y = 3------ADD

- 16x = - 48
x = 3

21 + 2y = 17
2y = - 4
y = - 2

x = 3 , y = - 2

7x+2y= 17 ......(1) -3(7x+2y=17)= -21x -6y=-34 ....(3)
5x+6y = 3........(2)
(2)+(3)= -16x= -31
x= 1.9375
7( 1.9375 )+2y=17
y=1.71875
(1.9375 , 1.71875 )

Solve for x in terms of y...

7x+2y=17
2y=17-7x
y=(17-7x)/2

Now, substitute into the second equation...

5x+6(17-7x)/2=3
5x+3(17-7x)=3
5x+51-21x=3
-16x+51=3
-16x=-48
x=3

Now, plug that back into the equation you got for y...
y=(17-7x)/2
y=(17-7*3)/2
y=(17-21)/2
y=-4/2
y=-2

7x + 2y = 17
7x = 17 - 2y
x = (17 - 2y)/7
5x = 5(17 - 2y)/7

5x + 6y = 3
5(17 - 2y)/7 + 6y = 3
7[(85 - 10y)/7 + 6y] = 7(3)
85 - 10y + 42y = 21
-10y + 42y = 21 - 85
32y = -64
y = -64/32
y = -2

7x + 2y = 17
7x + 2(-2) = 17
7x = 17 + 4
x = 21/7
x = 3

∴ x = 3 , y = -2

3,-2

7x + 2y = 17......... equation 1
5x + 6y = 3............ equation 2

Multiply equation 1 by -3.

-21x - 6y = -51

Add this to equation 2.

-21x - 6y + 5x + 6y = -51 + 3
-16x = -48
x = -48/-16
x = 3

7x + 2y = 17
7*3 + 2y = 17
21 + 2y = 17
2y = 17 - 21
2y = -4
y = -2

You answer: (3,-2)

7x + 2y = 17
5x + 6y = 3

Use Matrix Algebra:

Write as an augmented matrix:

[7 2 | 17]
[5 6 | 3 ]

Perform a gaussian elimination or LU decomposition. The row-reduced echelon form is

[1 0 | 3]
[0 1 | -2]

Therefore, the solution is (3,-2).