Question

A system of equations is given below. {x−2y=63x+4y=5 Which of the following systems of equations has the same solution as the system given above? Responses {x−2y=64x=11 { x − 2 y = 6 4 x = 11 ⁢ ⁢ {x−2y=64x=17 { x − 2 y = 6 4 x = 17 ⁢ {x−2y=65x=11 { x − 2 y = 6 5 x = 11 ⁢ {x−2y=65x=17

Answer 1

The systems of equations that has the same solution as the given system is (d) x − 2y = 6, 5x = 17

Which systems of equations has the same solution as the given system

From the question, we have the following parameters that can be used in our computation:

x − 2y = 6

3x + 4y = 5

Multiply (1) by 2

2x − 4y = 12

3x + 4y = 5

Add both equations

5x = 17

So, we have

x = 17/5

x = 3.4

Also, we have

x − 2y = 6

3.4 − 2y = 6

2y = -2.6

y = -1.3

Testing the list of options, we have

x − 2y = 6

3.4 + 2 * 1.3 = 6 --- true

4x = 11 ⁢

4 * 3.4 = 11 --- false

x − 2y = 6

3.4 + 2 * 1.3 = 6 --- true

4x = 17

4 * 3.4 = 17 --- false

x − 2y = 6

3.4 + 2 * 1.3 = 6 --- true

5x = 11

5 * 3.4 = 11 --- false

x − 2y = 6

3.4 + 2 * 1.3 = 6 --- true

5x = 17

5 * 3.4 = 17 --- true

Hence, the systems of equations is (d) x − 2y = 6, 5x = 17