Which is the best approximate solution of the system of linear equations y = 1.5x - 1 and y = 1?
Options:
A. (0.33, 1)
B. (1.33, 1)
C. (1.83, 1)
D. (2.33, 1)
Answer (2)
The best approximate solution of the system of equations is (1.33, 1), corresponding to option B. This is derived by setting the two equations equal and finding the value of x, which is then substituted back to find y. Therefore, the final solution is approximately (1.33, 1).
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To find the best approximate solution of the system of linear equations given by y = 1.5 x − 1 and y = 1 , we need to find where these two lines intersect.
Substitute the value of y from the second equation into the first equation :
1 = 1.5 x − 1
Solve for x :
Add 1 to both sides of the equation:
1 + 1 = 1.5 x
2 = 1.5 x
Divide both sides by 1.5 to solve for x :
x = 1.5 2
x ≈ 1.33
Determine the corresponding y value :
Since the given equation is y = 1 , the y value of the intersection point remains 1.
Therefore, the approximate solution to this system is ( 1.33 , 1 ) .
The correct multiple choice option is: (B) (1.33, 1) . This option matches the calculated intersection point of the given lines.
