Answer:
B
Step-by-step explanation:
4x-5y=2 ...(1)
10x-21y=10 ...(2)
(1)+2(2) gives
24x-47y=22
The equivalent system for the given system of equations is 4x − 5y = 2, and 10x − 21y = 10 is 4x − 5y = 2 and 24x − 47y = 22
We have to determine, the equivalent system for the given system of equations is 4x − 5y = 2, and 10x − 21y = 10.
According to the question,
System of equation; 4x − 5y = 2, and 10x − 21y = 10.
To determine the equivalent relation following all the steps given below.
From equation 1,
[tex]4x - 5y = 2\\\\4x = 2 +5y\\\\x = \dfrac{2+5y}{4}[/tex]
Substitute the value of x in equation 2,
[tex]10(\dfrac{2+5y}{4} )- 21y= 10\\\\10 + 25y - 42y = 10 \times 2\\\\10 -17y = 20\\\\-17y = 20-10\\\\-17y = 10\\\\ y = \dfrac{-10}{17}[/tex]
Substitute the value of y in equation 1,
[tex]4x - 5(\dfrac{-10}{17}) = 2\\\\68x + 50 = 34\\\\68x = 34-50\\\\68x = -16\\\\x = \dfrac{-16}{68}\\\\x = \dfrac{-4}{17}[/tex]
The equation is equivalent to given relation which satisfies the value of x and y is,
[tex]-47(\dfrac{-10}{17} )+24 (\dfrac{-4}{17})= 22\\\\\dfrac{470-96}{17} = 22\\\\\dfrac{374}{17} = 22\\\\22 = 22[/tex]
Hence, The equivalent system for the given system of equations is 4x − 5y = 2, and 10x − 21y = 10 is 4x − 5y = 2 and 24x − 47y = 22.
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