This is Algebra btw. For the functions defined above, fill in the table of values.

Explain how we can find the solution to the system of equations using the table.​

Given equations;

y₁ = 3x - 8               -------------------(i)

y₂ = 0.5x + 7          --------------------(ii)

To fill the table, substitute the values of x into equations (i) and (ii)

=> At x = 0

y₁ = 3(0) - 8 = -8

y₂ = 0.5(0) + 7 = 7

=> At x = 1

y₁ = 3(1) - 8 = -5

y₂ = 0.5(1) + 7 = 7.5

=> At x = 2

y₁ = 3(2) - 8 = -2

y₂ = 0.5(2) + 7 = 8

=> At x = 3

y₁ = 3(3) - 8 = 1

y₂ = 0.5(3) + 7 = 8.5

=> At x = 4

y₁ = 3(4) - 8 = 4

y₂ = 0.5(4) + 7 = 9

=> At x = 5

y₁ = 3(5) - 8 = 7

y₂ = 0.5(5) + 7 = 9.5

=> At x = 6

y₁ = 3(6) - 8 = 10

y₂ = 0.5(6) + 7 = 10

=> At x = 7

y₁ = 3(7) - 8 = 13

y₂ = 0.5(7) + 7 = 10.5

=> At x = 8

y₁ = 3(8) - 8 = 16

y₂ = 0.5(8) + 7 = 11

=> At x = 9

y₁ = 3(9) - 8 = 19

y₂ = 0.5(9) + 7 = 11.5

=> At x = 10

y₁ = 3(10) - 8 = 22

y₂ = 0.5(10) + 7 = 12

The complete table is attached to this response.

(ii) To find the solution of the system of equations using the table, we find the value of x for which y₁ and y₂ are the same.

As shown in the table, that value of x = 6. At this value of x, the values of y₁ and y₂ are both 10.