Respuesta :
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
[tex]x = \frac{38}{11}[/tex]
[tex]y = 3x - 8 = \frac{3*38}{11} - \frac{88}{11} = \frac{26}{11}[/tex]
Now, we have to verify which of these systems have this answer:
4x − 5y = 2
13x − 8y = 4
13x - 8y = 4
[tex]13\frac{38}{11} - 8\frac{26}{11} = \frac{286}{11} \neq 4[/tex]
4x − 5y = 2
10x + 3y = 15
10x + 3y = 15
[tex]10\frac{38}{11} + 3\frac{26}{11} = \frac{458}{11} \neq 15[/tex]
4x − 5y = 2
13x − 8y = 26
4x - 5y = 2
[tex]4\frac{38}{11} - 5\frac{26}{11} = \frac{22}{11} = 2[/tex]
13x - 8y = 26
[tex]13\frac{38}{11} - 8\frac{26}{11} = \frac{286}{11} = 26[/tex]
This is the correct answer
So this is the correct answer
4x − 5y = 2
7x + 6y = 10
