Ask a New Question
Menu

Billy graphed the system of linear equations to find an approximate solution.

y = A system of equations. y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction. y equals StartFraction 3 over 4 EndFraction x minus 3.x +
y = x – 3

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 points are possible approximations for this system? Select two options.

(1.9, 2.5)
(2.2, –1.4)
(2.2, –1.35)
(1.9, 2.2)
(1.9, 1.5)

1 answer

To find the points that are possible approximations for the intersection of the two lines represented by the equations given, we look for points that are close to where the two lines intersect.

From the description:

  • The first line, \( y = -\frac{7}{4}x + \frac{5}{2} \), has a y-intercept of 2.5 and passes through approximately (2.2, -1.4).
  • The second line, \( y = \frac{3}{4}x - 3 \), has a y-intercept of -3 and also passes through (2.2, -1.4).

Since both equations pass through the point (2.2, -1.4), it is definitely one possible approximation for the intersection. Now, we will analyze the rest of the options:

  1. (1.9, 2.5): This point does not fit well within the range of the intersection seen on the graph.
  2. (2.2, –1.4): This point lies on both lines. (Selected)
  3. (2.2, –1.35): This point is very close to (2.2, -1.4) and is likely to be around the intersection as well. (Selected)
  4. (1.9, 2.2): This point does not align closely with the intersection of the lines.
  5. (1.9, 1.5): This point is not near the intersection point either.

Based on the analysis, the two options that are possible approximations for the system are:

  • (2.2, –1.4)
  • (2.2, –1.35)