How do solve the following linear system?: 2x+5y=1 , 4x+3y=1 ?

1 Answer
Mia
Jul 17, 2016

x=1/7 and y = 1/7

Explanation:

To solve a system of two unknowns there are more than a way.
Get rid of x and then we solve for y by applying the following method:

Method:

1) Multiply one of the equations by an integer in such a way to obtain opposite coefficients of x in both equations.

2)Add both equations to obtain an equation with one unknown y.

3) solve for y

4) Substitute y in one of the original equations (equation before multiplying the integer).

5) Solve for x.

Let's apply this method:
2x + 5y = 1 (eq.1)

4x + 3y = 1 (eq2)

Multiply eq.1 by -2 so we have :
- 4x - 10y = -2 (eq1)
4x + 3y = 1 (eq2)

Adding both equations WEl have:
-7y = -1
then y = 1/7

Substitute y in eq.2 :
4x + 3(1/7) = 1
rArr 4x + 3/7 = 1
rArr 4x = 1- 3/7
rArr 4x = 4/7
rArr x = 1/7

We can check if the values of x and y are right by substituting them in one of the equations
Substitute the values in eq1 :
2(1/7) + 5(1/7) =? 1
2/7 + 5/7 =? 1
7/7 =?1 true

Therefore , x = 1/7 and y = 1/7

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