forte2001
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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?

Verified Answer :

meerkat18

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


calculista

we have that

System A

\(x+3y=11\)

System B

\(5x-y=17\)

Step \(1\)

Multiply System B by \(3\)

\(3*(5x-y)=3*17\)

\(15x-3y=51\)

Step \(2\)

Find the sum system A and system B

\(x+3y=11\)

\(15x-3y=51\\ ------\)

\(16x=62\)

\(x=\frac{62}{16} \\ \\ x=\frac{31}{8}\)

\(x=3.875\)

Find the value of y

\(5x-y=17\)

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

therefore

the answer is

the solution of the system is the point \((3.875,2.375)\)

see the attached figure


View image calculista

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