x = 3, y = 4
Explanations:Let us find the equations represented by each of the tables
Calculate the slope for table 1 selecting the points (2, 5) and (3, 4)
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{4-5}{3-2} \\ \text{m = }\frac{-1}{1} \\ m\text{ = -1} \end{gathered}[/tex]The equation of the line is given as:
[tex]\begin{gathered} y-y_1=m(x-_{}x_1) \\ y\text{ - 5 = -1(x - 2)} \\ y\text{ - 5 = -x + 2} \\ y\text{ = -x + 2 + 5} \\ y\text{ = -x + 7} \end{gathered}[/tex]The equation represented by the first table is y = -x + 7
Calculate the slope for table 2 by selecting the points (0, 1) and (1, 2)
[tex]\begin{gathered} m\text{ = }\frac{2-1}{1-0} \\ m\text{ = 1} \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 1 = 1 (x - 0)} \\ y\text{ - 1 = x} \\ y\text{ = x + 1} \end{gathered}[/tex]The equation represented by the second table is y = x + 1
The system of equations is:
y = -x + 7..........(1)
y = x + 1...........(2)
Equating equations (1) and (2)
-x + 7 = x + 1
x + x = 7 - 1
2x = 6
x = 6/2
x = 3
Substitute the value of x into equation (2)
y = 3 + 1
y = 4
The solution to the system of equations is x = 3, y = 4