Question

Determine the equivalent system for the given system of equations.

Answer 1

Answer:

4x − 5y = 2

13x − 8y = 26

Step-by-step explanation:

The equivalent system must have the same solution as the given system of equations:

4x − 5y = 2

3x − y = 8

Here we have that:

y = 3x - 8

4x - 5y = 2

4x - 5(3x - 8) = 2

4x - 15x + 40 = 2

-11x = -38

$x = \frac{38}{11}$

$y = 3x - 8 = \frac{3*38}{11} - \frac{88}{11} = \frac{26}{11}$

Now, we have to verify which of these systems have this answer:

4x − 5y = 2

13x − 8y = 4

13x - 8y = 4

$13\frac{38}{11} - 8\frac{26}{11} = \frac{286}{11} \neq 4$

4x − 5y = 2

10x + 3y = 15

10x + 3y = 15

$10\frac{38}{11} + 3\frac{26}{11} = \frac{458}{11} \neq 15$

4x − 5y = 2

13x − 8y = 26

4x - 5y = 2

$4\frac{38}{11} - 5\frac{26}{11} = \frac{22}{11} = 2$

13x - 8y = 26

$13\frac{38}{11} - 8\frac{26}{11} = \frac{286}{11} = 26$

This is the correct answer

So this is the correct answer

4x − 5y = 2

7x + 6y = 10

Answer 2

Answer:

The answer is

(4x - 5y = 2) and (13x - 8y =26)