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

Question

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

1 Answer

Impact of this question

2807 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-02T20:13:10

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

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question