Which is the best approximate solution of the system of linear equations [tex]\( y = 1.5x - 1 \)[/tex] and [tex]\( y = 1 \)[/tex]?

A. [tex]\((0.33, 1)\)[/tex]
B. [tex]\((1.33, 1)\)[/tex]
C. [tex]\((1.83, 1)\)[/tex]
D. [tex]\((2.33, 1)\)[/tex]



Answer :

To solve the system of linear equations [tex]\( y = 1.5x - 1 \)[/tex] and [tex]\( y = 1 \)[/tex]:

1. We start with the second equation where [tex]\( y = 1 \)[/tex]:
[tex]\[ y = 1 \][/tex]

2. Using the first equation [tex]\( y = 1.5x - 1 \)[/tex], we substitute [tex]\( y = 1 \)[/tex]:
[tex]\[ 1 = 1.5x - 1 \][/tex]

3. To isolate [tex]\( x \)[/tex], we add 1 to both sides of the equation:
[tex]\[ 1 + 1 = 1.5x \][/tex]
[tex]\[ 2 = 1.5x \][/tex]

4. Now, divide both sides by 1.5 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2}{1.5} \][/tex]

5. Simplifying [tex]\(\frac{2}{1.5}\)[/tex]:
[tex]\[ x = \frac{2}{1.5} \approx 1.3333 \][/tex]

Therefore, the approximate solution for [tex]\( (x, y) \)[/tex] when [tex]\( y = 1 \)[/tex] is:
[tex]\[ (x, y) \approx (1.33, 1) \][/tex]

So, the best approximate solution of the system of linear equations [tex]\( y = 1.5x - 1 \)[/tex] and [tex]\( y = 1 \)[/tex] is:
[tex]\((1.33, 1)\)[/tex].