Question

Determine the equivalent system for the given system of equations. 4x - 5y = 2 3x - y = 8

Answer 1

Solving the system of equations we get solution set (38/11,26/11)

Step-by-step explanation:

We need to solve the system of equations:

$4x - 5y = 2\\3x - y = 8$

Let:

$4x - 5y = 2\,\,\,eq(1)\\3x - y = 8\,\,\,eq(2)$

Multiply equation 2 with 5 and subtract both equations to find value of x:

$4x - 5y = 2\\15x - 5y = 40\\-\,\,\,\,+\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\\--------\\-11x=-38\\x=\frac{-38}{-11}\\x=\frac{38}{11}$

So, value of x = 38/11

Now, finding y:

Putting value of x in equation 2

$3x-y=8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-y=8\\-y=8-\frac{114}{11}\\-y=\frac{8*11-114}{11}\\-y=\frac{88-114}{11}\\-y=\frac{-26}{11}\\y=\frac{26}{11}$

So, value of y = 26/11

So, Solving the system of equations we get solution set (38/11,26/11)

Keywords: System of equations

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