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a) Use the diagram to work out the solution to these simultaneous equations: y = 2x + 3 y = -x + 9 b) Substitute your a value into each of the equations and solve to find y. What do you notice about i) the value of y in each equation? ii) the value of y compared to the solution in part a)? 10- 9 8 7- 6 5 3 2 1 0 1 2 3 y=2z+3 U-249 9 10​

a) Use the diagram to work out the solution to these simultaneous equations: y = 2x-example-1
User Askewchan
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Answer:

a) 2x + 3 = -x + 9

3x = 6

x = 2

b) 2(2) + 3 = 7, -2 + 9 = 7

i. The value of y is the same.

ii. The value of y is the same.

User Jesse Millikan
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a) The solution to the simultaneous equations is x = -2.0, y = -1.0.

b) When x = 15, the values of y are y1 = 33 and y2 = -6.

The runner's speed increased steadily during the first three seconds of the race. The table provides the speed at half-second intervals. To estimate the distance traveled, we can calculate the lower and upper estimates.

According to the given table, the runner's speed is recorded at half-second intervals. We can calculate the distance traveled by the runner by approximating the area under the curve of the speed-time graph. Since the speed is given at half-second intervals, we can divide the time interval into six smaller intervals of half a second each.

To estimate the lower and upper bounds for the distance traveled, we can use the trapezoidal rule. The trapezoidal rule states that the area under a curve can be approximated by dividing it into trapezoids. The formula for calculating the area of a trapezoid is (1/2) × (base1 + base2) × height. In this case, the bases are the speeds at consecutive time intervals, and the height is the time interval of half a second.

Comparing the values of y, we notice that:

The values of y in each equation are different.

The values of y in each equation are not equal to the solution in part a).

The reason for this is that the lines intersect at a different point than the point where x = 15.

Part Value of y

Equation 1 33

Equation 2 -6

Solution -1.0

User BaronGrivet
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