Solve the system of equations.
-x + 2y + 2z + w = -3.5 x + y + z + w = -2.5
A) (-w - 1.5, -z - 1, z, w)
B) (-w + 1, -z - 3.5, z, w)
C) (-w - 1.5, -w - 1, w, w)
D) (w - 1.5, z - 1, -z, -w)

Question

Quizplus · Accepted Answer

Subtracting the second equation from the first gives: $y + z = -1$. This system does not provide a unique solution for $x, y, z,$ and $w$, but we can express $x, y,$ and $z$ in terms of $w$. From the second equation, $x = -2.5 - y - z - w$. Substituting $y + z = -1$ into this expression for $x$ gives $x = -w - 1.5$. Similarly, $y$ can be expressed as $y = -z - 1$, keeping $z$ and $w$ as variables. Thus, the correct representation in terms of $w$ and $z$ is option A: $(-w - 1.5, -z - 1, z, w)$.

Solve the System of Equations