Question

what is the solution to the system of equations?
$y = 1.5x - 4$
$y=-x$
(-1.6, 1.6)
(-1.5, 1.5)
(1.5, -1.5)
(1.6, -1.6)

Explanation:

Step1: Set the two equations equal

Since \(y = 1.5x - 4\) and \(y=-x\), we set \(1.5x - 4=-x\).

Step2: Add \(x\) to both sides

\(1.5x+x - 4=-x+x\), which simplifies to \(2.5x-4 = 0\).

Step3: Add 4 to both sides

\(2.5x-4 + 4=0 + 4\), getting \(2.5x=4\).

Step4: Solve for \(x\)

\(x=\frac{4}{2.5}=\frac{4\times2}{2.5\times2}=\frac{8}{5}=1.6\).

Step5: Find \(y\) value

Substitute \(x = 1.6\) into \(y=-x\), so \(y=-1.6\).

Answer:

\((1.6,-1.6)\)