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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

5 answers

To find the best estimate for the solution of the system of linear equations from the graph, look for the point where the two lines intersect. This intersection point represents the values of \(x\) and \(y\) that satisfy both equations.

Since I do not have the image to reference the graph as requested, you will need to find the point of intersection on the graph. Once you've identified that point, you can input the coordinates or values into the designated response area.

If you provide me with the coordinates of the intersection point shown on the graph, I can help confirm if that's the correct response.

x + y = 975
0.05 + 0.12y = 111

It looks like there was a small mistake in the second equation you've provided. The correct second equation based on your original investment problem is:

\[ 0.05x + 0.12y = 111 \]

Now, let's solve the system of equations to find the values of \( x \) and \( y \).

  1. The first equation is: \[ x + y = 975 \]

  2. The second equation is: \[ 0.05x + 0.12y = 111 \]

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 975 - x \]

Now, substitute \( y \) in the second equation: \[ 0.05x + 0.12(975 - x) = 111 \]

Distributing \(0.12\): \[ 0.05x + 117 - 0.12x = 111 \]

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

Subtract 117 from both sides: \[ -0.07x = 111 - 117 \] \[ -0.07x = -6 \]

Now, divide both sides by -0.07: \[ x = \frac{-6}{-0.07} = \frac{6}{0.07} \approx 85.71 \]

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

So the solution to the system of equations is approximately: \[ x \approx 85.71 \quad (5% \text{ investment}) \] \[ y \approx 889.29 \quad (12% \text{ investment}) \]

If you need to plot this on a graph, the best estimate for the solution would be around the point \((85.71, 889.29)\).

If you have specific coordinates from a graph or a range for the estimate, please provide that, or you can enter this point in the response area as your best estimate.

choose: (880,120) (120, 880) (85, 900) (900, 85)

To find the best estimate for the solution based on the options provided, we need to analyze which point approximates the calculated values of \( x \approx 85.71 \) and \( y \approx 889.29 \).

Now let's compare the options:

  1. (880, 120): This point does not match the expected values at all.
  2. (120, 880): This point is also quite far from the expected values.
  3. (85, 900): This point is close to our computed values, with \( x \) being close to 85 and \( y \) being somewhat close at 900.
  4. (900, 85): This point is not a good fit since the \( y \) value is too low compared to the expected total.

Given the values we calculated, the point that best represents an estimate for the solution of the system of equations is:

(85, 900)

So, you should select (85, 900) as the best estimate to the solution of the system of linear equations.