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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