How do you solve $3 x - y = 8$ $3x - y = 8$ and $- 2 x + y = 4$ $-2x + y = 4$ using matrices?

Question

2195 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-10T17:44:45

Please see the explanation.

Write $3 x - y = 8$ $3x - y = 8$ as the first row in an augmented matrix:

$[ (3, -1, |, 8) ]$

Write $-2x + y = 4$ as the second row:

$[ (3, -1, |, 8), (-2, 1,|, 4) ]$

Add row 2 to row 1:

$[ (1, 0, |, 12), (-2, 1,|, 4) ]$

Multiply row 1 by 2 and add to row 2:

$[ (1, 0, |, 12), (0, 1,|, 28) ]$

The above augmented identity matrix translates into:

$x = 12 and y = 28$

check by substituting into the given equations:

$3(12) - 28 = 8$
$-2(12) + 28 = 4$

$8 = 8$
$4 = 4$

This checks

How do you solve 3x - y = 83x−y=83x - y = 8 and -2x + y = 4−2x+y=4-2x + y = 4 using matrices?