Solve the system of equations.
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A)x = 2 - 5z, and y = 3z - 1, where z is any real number or { , and y = 3z - 1, where z is any real number}
B)x = 2 + 7z, and y = -3z - 1, where z is any real number or , and y = -3z - 1, where z is any real number}
C)x = -2 - 7z, and y = -3z -1, where z is any real number or and y = -3z -1, where z is any real number}
D)x = 1 - 5z, and where z is any real number or and , where z is any real number

Question

Solve the system of equations.
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A)x = 2 - 5z, and y = 3z - 1, where z is any real number or { , and y = 3z - 1, where z is any real number} 
B)x = 2 + 7z, and y = -3z - 1, where z is any real number or , and y = -3z - 1, where z is any real number} 
C)x = -2 - 7z, and y = -3z -1, where z is any real number or and y = -3z -1, where z is any real number} 
D)x = 1 - 5z, and where z is any real number or and , where z is any real number

Quizplus · Accepted Answer

We can see that both options in A give us a value for y in terms of z, which means we can substitute it into the x equation to solve for x in terms of z. This gives us a unique solution for x and y for any value of z, which satisfies the system of equations. On the other hand, in options B, C, and D, one of the variables is not expressed in terms of a single parameter, which means we cannot solve for both variables in terms of a single parameter. Therefore, the best choice is A. From the first equation, we can solve for z as z=(2-x)/5. Substituting this into the second equation, we get y=3((2-x)/5)-1 which simplifies to y= (6-3x)/5 -1 or y=(6-3x-5)/5=-3x/5+1. Thus we have x = 2 - 5z and y = 3z - 1 or x = (2-x)/5 and y = -3x/5+1 where z is any real number.

Solve the System of Equations