Question

Claire made tables of values to solve a system of equations. First, she found

that the x-value was between 0 and 1. Next, she found that it was between 0.5

and 1. Then she made this table.

x | y= 5x-3y=-7x+8

0.5

-0.5

4.5

0.6

0

3.8

0.7

0.5

3.1

0.8

1

2.4

0.9

1.5

1.7

1.0

2

1

Which ordered pair is the best approximation of the solution?

Answer 1

To determine the best approximation of the solution, we can substitute each value of x from the table into the two equations and check which ordered pair satisfies both equations the closest.

Using the table values, we can see that when x is 0.8, the values of y for both equations are closest to the given values. So, the best approximation of the solution is the ordered pair (x, y) = (0.8, 1.6), since it satisfies both equations with the closest values:

5x - 3y = 5(0.8) - 3(1.6) = 4 - 4.8 = -0.8

-7x + 8y = -7(0.8) + 8(1.6) = -5.6 + 12.8 = 7.2

Therefore, the ordered pair (0.8, 1.6) is the best approximation of the solution.

Explanation:

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