Answer:
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).
