Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A. A. x + 3y = 11 → x + 3y = 11 5x − y = 17 → 15x − 3y = 51 15x = 62 B. x + 3y = 11 15x = 62 What is the solution to both systems A and B?

A.)
x + 3y = 11
5x - y = 17 ⇒ 15x - 3y = 51
15x = 62

B.) x + 3y = 11
15x = 62

x + 3y = 11
5x - y = 17

x = 11 - 3y
5x - y = 17
5(11-3y) - y = 17
55 - 15y - y = 17
-16y = 17 - 55
-16y = -38
y = -38/-16
y = 2.375

x = 11 - 3y
x = 11 - 3(2.375)
x = 11 - 7.125
x = 3.875

x = 3.875 ; y = 2.375

x + 3y = 11
3.875 + 3(2.375) = 11
3.875 + 7.125 = 11
11 = 11

Answer Link

calculista calculista · Answer 2 · 2018-08-15T02:29:46+02:00

we have that

System A

[tex] x+3y=11 [/tex]

System B

[tex] 5x-y=17 [/tex]

Step [tex] 1 [/tex]

Multiply System B by [tex] 3 [/tex]

[tex] 3*(5x-y)=3*17 [/tex]

[tex] 15x-3y=51 [/tex]

Step [tex] 2 [/tex]

Find the sum system A and system B

[tex] x+3y=11 [/tex]

[tex] 15x-3y=51\\ ------ [/tex]

[tex] 16x=62 [/tex]

[tex] x=\frac{62}{16} \\ \\ x=\frac{31}{8} [/tex]

[tex] x=3.875 [/tex]

Find the value of y

[tex] 5x-y=17 [/tex]

[tex] 5x-y=17\\ y=5*\frac{31}{8} -17\\ \\ y=\frac{(155-8*17)}{8} \\ \\ y=\frac{19}{8} \\ \\ y=2.375 [/tex]

therefore

the answer is

the solution of the system is the point [tex] (3.875,2.375) [/tex]

see the attached figure