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A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4)

Which is the best approximate solution of the system of linear equations y = 1.5x – 1 and y = 1?

(0.33, 1)
(1.33, 1)
(1.83, 1)
(2.33, 1)

1 answer

To find the best approximate solution of the system of linear equations given by \( y = 1.5x - 1 \) and \( y = 1 \), we can solve for \( x \) where these two equations intersect.

  1. Set the equations equal to each other: \[ 1.5x - 1 = 1 \]

  2. Solve for \( x \): \[ 1.5x = 1 + 1 \] \[ 1.5x = 2 \] \[ x = \frac{2}{1.5} = \frac{4}{3} \approx 1.33 \]

  3. Now, substitute \( x \) back into either equation to find \( y \). We can use \( y = 1 \): \[ y = 1 \]

Thus, the approximate solution of the system of linear equations is \( (1.33, 1) \).

The answer is: (1.33, 1)