Question

Determine the equivalent system for the given system of equations:

Answer 1

Answer:

They are an equivalent system and the values are x=17/37 and y=-16/37

Step-by-step explanation:

Systems of equations that have the same solution are called equivalent systems.

Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.

(-4)*(5x + 3y = 1) → -20x - 12y = -4

(5)*(4x − 5y = 4) → 20x - 25y =20

Add the last 2 eq →  -37y= 16 →  y= - 16/37

replace this value in any equation of the system.

5x + 3(-16/37) = 1 →  x= (1 +48/37)/ 5 =(37/37 + 48/37)/5=(85/37)/5 = 17/37

We have x and y values. Replace this values in both equation and verify the result

5x + 3y = 1  → 85/37 -48/37 =37/37=1

4x − 5y = 4 → 68/37 + 80/37= 148/37= 4

So, in fact, they are a equivalent system