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How do you solve $5 x - 2 y = 10$ $5x - 2y = 10$ and $3 x + 2 y = 6$ $3x + 2y = 6$ using substitution?

1 Answer

May 25, 2018

$x = 2 and y = 0$ $x=2 and y=0$

Explanation:

I wonder why you would want to solve this by substitution when elimination is an easier and more obvious method because of the $- 2 y and + 2 y$ $-2y and +2y$ terms.?

Make a single variable the subject:
$3 x + 2 y = 6 \to 2 y = 6 - 3 x \to y = 3 - \frac{3 x}{2}$ $3x +2y =6 " "rarr 2y = 6-3x" "rarr color(blue)(y = 3-(3x)/2)$

Substitute this expression for $y$ $y$ in the first equation:

$5 x - 2 y = 10$ $5x -2color(blue)(y) =10$

$5 x - 2 (3 - \frac{3 x}{2}) = 10$ $5x -2(color(blue)(3-(3x)/2)) =10$

$5 x - 6 + 3 x = 10$ $5x -6+3x =10$

$8 x = 16$ $8x = 16$

$x = 2$ $x =2$

$y = 3 - \frac{3 (2)}{2}$ $color(blue)(y = 3-(3(2))/2$

$y = 0$ $y=0$

Compare the Elimination method

$" "5x-2y=10" "....A$
$" "ul(3x+2y =6)" ".....B$
$" "8x " "=16" "larr A+B$
$color(white)(xxxxx.x) x=2$

Substitute in $B$

$3x+2y=6$
$3(2)+2y=6$
$cancel6+2y = cancel6$
$y=0$

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