Final answer:
To find the equivalent system of equations, we can multiply the equations by appropriate constants and eliminate a variable. The equivalent system is 2x + 3y = 7 and 8x - 4y = 4.
Step-by-step explanation:
To determine the equivalent system for the given system of equations, we need to eliminate one variable by multiplying the equations with appropriate constants. Multiplying the first equation by 2 and the second equation by 1 gives us:
4x + 6y = 14
4x - 2y = 4
Now, we can subtract the second equation from the first equation:
(4x + 6y) - (4x - 2y) = 14 - 4
Which simplifies to:
8y = 10
Dividing both sides by 8, we find that y = 5/4.
Plugging this value of y back into one of the original equations, like 2x + 3y = 7, we can solve for x:
2x + 3(5/4) = 7
Which simplifies to:
2x + 15/4 = 7
Multiplying both sides by 4 to get rid of the denominators, we have:
8x + 15 = 28
Subtracting 15 from both sides, we get:
8x = 13
Finally, dividing both sides by 8, we find that x = 13/8.
Therefore, the equivalent system of equations is:
2x + 3y = 7
8x - 4y = 4
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