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avatar+1405 

solve for x and y

2x+3y=9

x-y=2

 Oct 23, 2017
 #1
avatar
+1

Solve the following system:
{2 x + 3 y = 9 | (equation 1)
x - y = 2 | (equation 2)

 

Subtract 1/2 × (equation 1) from equation 2:
{2 x + 3 y = 9 | (equation 1)
0 x - (5 y)/2 = (-5)/2 | (equation 2)

 

Multiply equation 2 by -2/5:
{2 x + 3 y = 9 | (equation 1)
0 x+y = 1 | (equation 2)

 

Subtract 3 × (equation 2) from equation 1:
{2 x+0 y = 6 | (equation 1)
0 x+y = 1 | (equation 2)

Divide equation 1 by 2:


{x+0 y = 3 | (equation 1)
0 x+y = 1 | (equation 2)
x = 3            and               y = 1

 Oct 23, 2017
 #2
avatar+98196 
+2

2x +3y = 9   (1)

x - y = 2     add y to both sides  → x =  2 + y     (2)

 

Sub ( 2) into ( 1)

 

2 ( 2 + y)  + 3y  =  9     simplify

 

4 + 2y + 3y  =  9

 

5y + 4  =  9       subtract  4 from each side

 

5y  =  5             divide both sides by 5

 

y = 1

 

Abd using (2)  ...   x = 2 + 1  = 3

 

 

cool cool cool

 Oct 23, 2017

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