# Solve by any algebraic method. A) 4x+3y= -2 -5x-2y=9 If there is no solution to this system of equations,state the reason. B) 2/3x+y=1 3 /4x+1/2y=3/4

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- `4x+3y = -2` and 2. `-5x - 2y = 9`

We must eliminate one of the variables (x and y) to enable us to solve this system of equations. We must first make one of the variables in each equation equal to the other. Remember with equations you can make any necessary changes as long as you change everything. So we will multiply 1. x 2 and 2. x 3 to create equation 3. and 4. - so that we can eliminate y:

3. `2(4x) +2(3y) = 2(-2)` and

4. `3(-5x)-3(2y) = 3(9)`

3. `therefore 8x + 6y = -4` and 4. `-15x - 6y = 27`

Eliminate y by adding the two equations together (3.+ 4.)

`8x + (-15x) +6y + (-6y) = -4 +27`

`-7x +0y = 23`

`therefore -7x= 23`

`therefore x= 23/-7`

Now substitute into any one of the previous equations to find y:

`4x + 3y = -2`

`therefore 4(23/-7) +3y = -2`

`therefore -92/7 +3y = -2`

`therefore 3y = -2+ 13 1/7`

`therefore 3y =78/7`

`therefore y = (78/7)/3`

`therefore y = 78/7 times 1/3` (equivalent to the previous 78/7/3)

`therefore y = 78/21`

` therefore y = 26/7or 3 5/7`

`( - 23/7; 26/7)`

**The solution to the system of equations is x= -23/7 and y = 26/7**

**Sources:**

`a)`

`4x+3y = -2`

`-5x-2y =9```

`4x+3y-5x-2y= -2 +9`

`y-x = 7`

`4y-4x= 28`

`4x+3y+4y-4x=-2+28`

`7y= 26`

`y=26/7`

`x=y-7=26/7 -7 =(26-49)/7=-23/7`

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`b)`

``

`2/3 x +y = 1`

`3/4 x + 1/2 y = 3/4`

making ratio out:

`2x+3y=3`

`3x+2y=3`

subtracting second relation from first:

`2x+3y-(3x+2y)= 3 -3`

so:

`2x+3y -3x-2y = 0`

`y - x = 0` `x= y`

subistuing in the second relation we have now:

`5x= 3`

the solutions are: `x= y = 3/5`

`2/3 x+ y= 1`