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Chris put a total of $975 in two different investments, one that earned 5% interest and one that earned 12% interest. The total investment income was $111. If x represents the amount invested at 5% and y represents the amount invested at 12%, the system of linear equations that models the scenario is the following:

{x+y=9750.05x+0.12y=111


The system of linear equations is shown in the following graph.

Two lines are graphed on the coordinate plane.

Which point represents the best estimate to the solution of the system of linear equations?

(1 point)
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The point that is the best estimate to the solution of the system of linear equations is Response area.

1 answer

To solve the problem and identify the point that best estimates the solution of the system of linear equations, we need to analyze the equations provided:

  1. \( x + y = 975 \)
  2. \( 0.05x + 0.12y = 111 \)

In the context of a graph, these equations represent two lines in the coordinate plane. The solution to the system of equations is the point where the two lines intersect.

Since I cannot see the graph, the best approach is to find the intersection point (solution) of the two equations.

Step 1: Solving the system of equations

From the first equation: \[ y = 975 - x \]

Substituting \( y \) into the second equation: \[ 0.05x + 0.12(975 - x) = 111 \]

Expanding this gives: \[ 0.05x + 117 - 0.12x = 111 \]

Combine like terms: \[ -0.07x + 117 = 111 \]

Now, isolate \( x \): \[ -0.07x = 111 - 117 \] \[ -0.07x = -6 \] \[ x = \frac{-6}{-0.07} \] \[ x = 85.71 , (\text{approximately}) \]

Step 2: Finding \( y \)

Now substitute \( x \) back into the equation for \( y \): \[ y = 975 - 85.71 \approx 889.29 \]

Conclusion

The estimated solution to the system of equations is approximately \( (85.71, 889.29) \).

In your question, you would select the point that represents these values on the graph. The estimate might vary slightly depending on the accuracy of the graphing. Look for a point close to \( (85.71, 889.29) \) in the provided graph to determine which one best represents the solution.

If you need to choose a specific point from the responses available, please compare the values you see in the graph with the estimated \( (x, y) \) values calculated above.