Use an augmented matrix to solve the system. What is the value of x and y?

x + y = 5
3x – y = –1

(1, 4)
(1, 5)
(3, –1)
(5, –1)

Question

Use an augmented matrix to solve the system. What is the value of x and y?

  x + y = 5
3x – y = –1  

(1, 4)
(1, 5)
(3, –1)
(5, –1)

jim_thompson5910 · Answer

x + y = 5 
3x – y = –1


1      1      5
3    -1     -1


1      1      5
0    -4     -16           R2 - 3*R1 ----> R2


1      1      5
0      1     4           (-1/4)*R2 -----> R2


1      0     1          R1 - R2 -----> R1
0      1     4           


The right column represents the solutions for x and y.


So the solutions are x = 1 and y = 4 meaning that the solution is the ordered pair (1,4)