a) Use the diagram to work out the solution to these simultaneous equations: b) Substitute your x 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)? Y 10 9 8 7 6 5 4 3 32 y = 2x + 1 y = -x + 7 1 1 2 3 4 y=2x+1 5 y=-x +7 6 7 8 9 10

Question

22-11-2022
Mathematics

Answered

a) Use the diagram to work out the solution to these simultaneous equations: b) Substitute your x 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)? Y 10 9 8 7 6 5 4 3 32 y = 2x + 1 y = -x + 7 1 1 2 3 4 y=2x+1 5 y=-x +7 6 7 8 9 10

Answer :

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sqdancefan sqdancefan · Answer 1 · 2022-11-22T20:57:39-05:00

Answer:

(a) (x, y) = (2, 5)

(bi) y = 5, y = 5; the values are the same

(bii) the values are the same as in part (a)

Step-by-step explanation:

You want the solution and some observations about it for the system of equations ...

y = 2x +1
y = -x +7

a) Solution

The graph shows the lines cross at the point (x, y) = (2, 5).

The solution to the equations is (x, y) = (2, 5).

b) Values of y

i) For x=2, the value of y in the first equation is ...

y = 2(2) +1 = 4 +1 = 5

For x=2, the value of y in the second equation is ...

y = -(2) +7 = -2 +7 = 5

ii) The values of y are the same, and match the value we found in part (a).

__

Additional comment

The purpose of the exercise is to get you to see that the value of x that is the solution makes both equations have the same value of y, and that is the value of y that is the solution.

The graph is a plot of the y-value for each x-value. Where the lines cross, the y-values are the same for that x-value. That point of intersection of the lines is the solution to the system of equations: the values of x and y satisfy both equations at that point.