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].
