Question

which is the best approximate solution of the system of linear equations $y = 1.5x - 1$ and $y = 1$?\\(\circ\\) $(0.33, 1)$\\(\circ\\) $(1.33, 1)$\\(\circ\\) $(1.83, 1)$\\(\circ\\) $(2.33, 1)$

Explanation:

Step1: Substitute \( y = 1 \) into the first equation

We have the system \(

$$\begin{cases} y = 1.5x - 1 \\ y = 1 \end{cases}$$

\). Substitute \( y = 1 \) into \( y = 1.5x - 1 \), we get \( 1=1.5x - 1 \).

Step2: Solve for \( x \)

Add 1 to both sides of the equation \( 1 = 1.5x-1 \): \( 1 + 1=1.5x \), so \( 2 = 1.5x \). Then divide both sides by \( 1.5 \): \( x=\frac{2}{1.5}=\frac{4}{3}\approx1.33 \).

Step3: Determine the solution

Since \( y = 1 \) and \( x\approx1.33 \), the solution of the system is \( (1.33, 1) \).

Answer:

B. (1.33, 1)