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

Question

2293 views around the world

You can reuse this answer
Creative Commons License

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#