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

Nov 10, 2016

Explanation:

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

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

Write $- 2 x + y = 4$ 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:

$x = 12 \mathmr{and} y = 28$

check by substituting into the given equations:

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

$8 = 8$
$4 = 4$

This checks