Question

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A system of linear equations is given by the tables. x y -1 1 0 3 1 5 2 7 x y -2 -7 0 -1 2 5 4 11

Answer 1

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A system of linear equations is given by the tables.

x y

-1 1

0 3

1 5

2 7

x y

-2 -7

0 -1

2 5

4 11

The first equation of this system is y =

2

x + 3.

The second equation of this system is y = 3x −

1

.

The solution of the system is (

4

,

11

).

Explanation:

Answer 2

1) The first equation of the system is y = 2·x + 3

2) The second equation of the system is y = 3·x - 1

3) The solution of the system is (4, 11)

Explanation:

1) From the coordinates of the first table, we have;

The points of the y-coordinate have a common difference of two

The rate of change of the function using the first and the last point is given as follows;

Rate of change = Slope, m = (7 - 1)/(2 - (-1)) = 2

The, equation of the line in point and slope form is, y - 7 = 2 × (x - 2)

∴ The equation of the line in slope and intercept form is y = 2·x + 3

Therefore, the first equation of the system is y = 2·x + 3

2) Similarly from the coordinates of the second table, we have;

The points of the y-coordinate have a common difference of six

The rate of change of the function using the first and the last point is given as follows;

Rate of change = Slope, m = (11 - (-7))/(4 - (-2)) = 3

The, equation of the line in point and slope form is, y - 11 = 3 × (x - 4)

∴ The equation of the line in slope and intercept form is y = 3·x - 1

Therefore, the second equation of the system is y = 3·x - 1

3) Equating both equations in the system of equations to find a common solution gives;

2·x + 3 = 3·x - 1

∴ x = 4

From y = 3·x - 1 or y = 2·x + 3, we have the value of y at the solution point as y = 3 × 4 - 1 = 11 or 2 × 4 + 3 = 11

∴ y = 11 at point of the common solution of the system of equations

Therefore, the coordinates of the common point which is the solution of the system is (4, 11).