How do you solve the following system?: 2x + 3y = 1 , -3x + 7y = 1

2 Answers
Binayaka C.
May 19, 2018

Solution: x = 4/23 , y =5/23

Explanation:

2 x + 3 y =1 ; (1) , -3 x +7 y =1 ; (2) Multiplying equation

(1) by 3 and equation (2) by 2 we get,

6 x + 9 y =3 ; (3) , -6 x +14 y =2 ; (4) Adding equation

(3) and equation (4) we get, 23 y= 5 :. y =5/23. Putting

y =5/23 in equation (1) we get, 2 x +3*5/23=1 or

2 x=1-15/23 or 2 x = (23-15)/23 or 2 x =8/23 or x = 4/23

Solution: x = 4/23 , y =5/23 [Ans]

Bill Jorgensen
May 19, 2018

y=5/23

x=4/23

Explanation:

2x+3y=1
-3x+7y=1

Probably the easiest way to solve this is by elimination; notice there is a GCD of 2x and -3x of 6x so let's multiply both equations by 3 and 2 respectively:

3(2x+3y=1)
2(-3x+7y=1)

6x+9y=3
-6x+14y=2

now add the equations together, notice the x terms are eliminated:

23y=5

y=5/23

now use either original equations with the y value you found to solve for x:

2x+3(5/23)=1

x=4/23

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