# How do you find the solution set for -5x+3y=35 and 3x+2y=-21?

Aug 16, 2015

x = - 7 ; y = 0

#### Explanation:

-5x+3y=35 Take 35 to the LHS
-5x+3y - 35 = 0 ------------(1)

3x+2y= -21 Take 21 to the LHS
3x+2y + 21 = 0 --------------(2)

Let us try to eliminate 'y'

-5x+3y - 35 = 0 ------------(1) $\times$ 2
- 10x + 6y - 70 = 0 -------------(3)

3x+2y + 21 = 0 --------------(2) $\times$ 3
9x + 6y + 63 = 0 ---------------(4)

Since equations (3) and (4) are equal to 0

Their LHS must be equal to one another

• 10x + 6y - 70 = 9x + 6y + 63

Bring all the unknowns to LHS and take integers to the RHS
Simplify -
- 10x + 6y - 9x - 6y= 63 + 70
- 19x = 133
x = #133/(- 9) = - 7

Substitute x = -7 in equation (1)

-5( - 7) +3y - 35 = 0
35 + 3y - 35 = 0 [Simplify]
3y = 0
y = 0