How do you solve $5x + 3y = 46$ and $2x + 5y = 7$ using matrices?

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Answer 1 · 2017-02-15T02:49:05

Apply Gaussian Elimination/ Gauss-Jordan on an augmented matrix.

Convert the system into an augmented matrix like so: $[ (5, 3, 46), (2, 5, 7)]$

Simplify to Reduced Row or Row Echelon form using elementary row operations:

Gaussian Elimination Example (REF):
$[ (1, -7, 32), (2, 5, 7)]$

$[ (1, -7, 32), (0, 19, -57)]$

$[ (1, -7, 32), (0, 1, -57/19)]$

$[ (1, -7, 32), (0, 1, -3)]$

So $1x + -7y = 32$ and $y = -3$
Thus $x = 32 + 7(-3) = 11$

How do you solve 5x + 3y = 465x + 3y = 46 and 2x + 5y = 72x + 5y = 7 using matrices?