How do you solve 7x - 2y = 4 and 5y + 3x = 10?

1 Answer
Tony B
Aug 2, 2016

point of intersection#->(x,y)=(40/41,58/41)#

Explanation:

#color(blue)("Using first principles")#

There are various ways of solving this question type. What follows is just one of them.

Given:
#7x-2y=4# ...............................Equation(1)
#5y+3x=10# ............................Equation(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of "x)#

Consider equation (2)

Subtract #3x# from both sides giving:

#5y=10-3x#

Divide both sides by 5

#y=10/5-3/5x# ..............................Equation(3)
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using equation(3) substitute for y in equation (1)

#color(brown)(7x-2y=4)color(blue)(" "->" "7x-2(10/5-3/5x)=4#

#=>7x-4+6/5x=4#

#41/5x-4=4#

Add 4 to both sides

#41/5x=8#
Multiply both sides by #5/41#

#color(blue)(=>x=5/41xx8" " =" "40/41)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of ")#
#color(brown)("Using shortcuts method")#
Substitute #x=40/41# into equation(2)

#color(brown)(5y+3x=10color(blue)(" "->" "5y+3(40/41)=10))#

#y=58/41#

Tony B

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