How do you solve the following linear system: $x + 3 y = 8, 2 x + y = 15$ $x + 3y= 8, 2x + y = 15$ ?

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How do you solve the following linear system: $x + 3 y = 8, 2 x + y = 15$ $x + 3y= 8, 2x + y = 15$ ?

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Answer 1 · 2016-03-09T11:53:57

$x = \frac{37}{5}; y = \frac{1}{5}$ $color(blue)(x=37/5" ; "y=1/5)$

Explanation:

Given:
$x + 3 y = 8$ $x+3y=8$ ............................(1)
$2 x + y = 15$ $2x+y=15$ ..........................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The most straight forward way of dealing with this one is to make the coefficients of y the same and then subtract so that you only have 1 variable.

Multiply equation (2) by 3 then subtract, giving:

$6x+3y=45......................(2_a)$
$underline(color(white)(.)x+3y=8).........................(1)$
$5x+0color(white)(.)=37$

Divide both sides by 5 giving:

$color(blue)(x=37/5)$ ................................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~
Substitute for $x$ in equation (1)

$37/5+3y=8$

Subtract $37/5$ from both sides

$3y=8-37/5 = 3/5$

Divide both sides by 3

$color(blue)(y=1/5)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
$color(brown)(x+3y=8)color(green)(-> 37/5+3(1/5) = 8) color(red)( " True")$

$color(brown)(2x+y=15)color(green)(->2(37/5)+1/5=15)color(red)(" True")$

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How do you solve the following linear system: $x + 3 y = 8, 2 x + y = 15$ $x + 3y= 8, 2x + y = 15$ ?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you solve the following linear system: x + 3y= 8, 2x + y = 15 x+3y=8,2x+y=15 x + 3y= 8, 2x + y = 15 ?

1 Answer

Explanation:

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How do you solve the following linear system: $x + 3 y = 8, 2 x + y = 15$ $x + 3y= 8, 2x + y = 15$ ?