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Algebra 2 one question!?
5.Solve { x-2y=2
{3x-5y=9
by writing and solving a matrix equation. Show all your work.
2 Answers
- husoskiLv 77 years ago
The augmented matrix is:
[ 1 -2 | 2 ]
[ 3 -5 | 9 ]
How you solve it depends on what methods you have learned. Solving that system by elimination looks exactly like solving algebraically by elimination, but with matrix notation:
[ 1 -2 | 2 ]
[ 0 1 | 3 ] ... added (-3) times row 1 to row 3
[ 1 0 | 8 ]
[ 0 1 | 3 ] .... added 2 times row 2 to row 1
The final column is your solution: x=8, y=3. Check with:
(8) - 2(3) = 8-6 = 2 ... check
3(8) - 5(3) = 24-15 = 9 ... also good
Other methods include Cramer's Rule/Method (using determinants) and multiplication by the inverse matrix.
