Solve the following system of linear equations for the variables x and y:
3x - 2y = 7
2x + y = 4
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To solve the system of linear equations, we can use the method of substitution or the method of elimination.
First, let's solve using the method of substitution:
From the second equation, we can express y in terms of x by subtracting 2x from both sides:
y = 4 - 2x
Now substitute this expression for y in the first equation:
3x - 2(4 - 2x) = 7
Simplify the equation:
3x - 8 + 4x = 7
Combine like terms:
7x - 8 = 7
Add 8 to both sides:
7x = 15
Divide both sides by 7:
x = 15/7
Now, substitute this value of x back into either of the original equations to find y. Let's use the second equation:
2(15/7) + y = 4
Multiply 2 by 15/7:
30/7 + y = 4
Subtract 30/7 from both sides:
y = 4 - 30/7
To simplify, find a common denominator of 7:
y = (28/7) - (30/7)
y = -2/7
So the solution to the system of linear equations is x = 15/7 and y = -2/7.
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