6x-9y=25.5 and 7y-3x=-14 what is the solution of the system of equations?

Hi,

Multiply the second equation by 2 and it it to the first equation. Solve for y. Plug it back in to solve for x.

6x - 9y = 25.5
-3x + 7y = -14

6x - 9y = 25.5
2(-3x + 7y = -14 )

6x - 9y = 25.5
-6x + 14y = -28
----------------------
5y = =2.5
y = -.5

If y = -.5 and 6x - 9y = 25.5, then
6x - 9(-.5) = 25.5
6x + 4.5 = 25.5
6x = 21
x = 21/6 = 3.5

The answer is x = 3.5 and y = -.5. That is the point (3.5,-.5) <== ANSWER

I hope that helps!! :-)

6x - 9y = 25.5
- 6x + 14y = - 28-------ADD

5y = - 2.5
y = - 0.5

6x + 4.5 = 25.5
6x = 21
x = 3.5

x = 3.5 , y = - 0.5

Value of y:
6x - 9y = 25.5
4x - 6y = 17
6y = 4x - 17
y = (4x - 17)/6

7y - 3x = - 14
7y = 3x - 14
y = (3x - 14)/7

Value of x:
7(4x - 17) = 6(3x - 14)
28x - 119 = 18x - 84
10x = 35
x = 3.5

Value of y:
= (4[3.5] - 17)/6
= (14 - 17)/6
= - 3/6
= - 0.5

Answer: x = 3.5, y = - 0.5

Proof (equation 1):
6(3.5) - 9(- 0.5) = 25.5
21 + 4.5 = 25.5
25.5 = 25.5

Proof (equation 2):
7(- 0.5) - 3(3.5) = - 14
- 3.5 - 10.5 = - 14
- 14 = - 14

6x - 9y = 25.5 (1)
7y - 3x = -14 (2)

(2) x 2
14y - 6x = -28 (3)

(3) + (1)
6x - 9y + 14y - 6x = 25.5 - 28
5y = -2.5
y = -1/2

14y - 6x = -28
-7 - 6x = -28
21 = 6x
x = 7/2 = 3.5

(3.5, -.5)

y=(3x-14)/7
6x-(9(3x-14)/7)=25.5
42x-9(3x-14)=178.5
42x-27x+126=178.5
15x=52.5

x=3.5

7y-(3x3.5)=-14
7y=-3.5

y=-0.5

6x - 9y = 25.5
6x = 25.5 + 9y
x = (25.5 + 9y)/6
3x = 3(25.5 + 9y)/6

7y - 3x = -14
7y - 3(25.5 + 9y)/6 = -14
7y - (25.5 + 9y)/2 = -14
2[7y - (25.5 + 9y)/2] = 2(-14)
14y - 25.5 - 9y = -28
5y = -28 + 25.5
5y = -2.5
y = -2.5/5
y = -1/2 (-0.5)

6x - 9y = 25.5
6x - (-9/2) = 25.5
6x = 25.5 - 9/2
6x = 25.5 - 4.5
6x = 21
x = 21/6
x = 3 1/2 (3.5)