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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

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)

Step-by-step 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).

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,