Solve the simultaneous equations

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

y - 14x/9= - 24/9

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We'll put the equation of the lines in the general form:

ax + by + c = 0

The first equation is:

7x-2y-17=0

The second equation is:

14x-9y-24=0

We'll form the system:

7x-2y-17=0

We'll add 17 both sides:

7x - 2y = 17 (1)

14x-9y-24=0

We'll add 24 both sides:

14x - 9y = 24 (2)

We'll solve the system using elimination method. For this reason, we'll multiply (2) by -2 and we'll add the resulting equation to (1):

-14x + 4y = -34 (3)

(1) + (3): 14x - 9y - 14x + 4y = 24 - 34

We'll eliminate and combine like terms:

-5y = -10

We'll divide by -5:

**y = 2**

We'll substitute y in (1):

14x - 9y = 24

14x - 18 = 24

14x = 24 + 18

14x = 42

7x = 21

**x = 3**

**The system has the solution {3,2}. **

To solve the simultaneous equations:

- 7x/2 + y= - 17/2...(1)

y - 14x/9= - 24/9....(2)

Eq(1) - eq (2) eliminates y:

-7x/2 +y -y +14x/9 = -17/2 +24/9

x(-7/2 +14/9) = (-17*9+24*2)/18)

x(-63 +28)/18 = (-105)/18

-35x = 105

x = 105/35 = 3

So we put x = 3 in y - 14x/9= - 24/9 and we get:

y - 14*3/9 = -24/9

y = -24/9+14*3/9 = 18/9 = 2

So x = 3 and y = 2.

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

y - 14x/9= - 24/9

First we will rewrtie both equations to get rid of the denominator:

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

Let us multiply by 2:

==> -7x + 2y = -17 ........(1)

For the second equations:

y- 14x/9 = -24/9

Multiply by 9:

==> 9y - 14x = -24

==> -14x + 9y = -24 .............(2)

Now we will solve the system :

Let ys mutiply (1) by -2 and add t0 *2):

==> -2 *(1) = -2 ( -7x + 2y = -17)

= 14x - 4y + 34...........(3)

Now add (3) to (2):

==> 5y = 10

Divide by 5:

**==> y = 2**

**Now to find x we will substitue in (3):**

14x - 4y = 34

14x - 4*2 = 34

==> 14x = 34 + 8

==> 14x = 42

**==> x = 3**

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