the tables represent two linear functions in a system. what is the solution to this system? (1,0) (1,6)…

Explanation:

Step1: Find the equation of the first line

Use the slope formula (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(0,10)) and ((x_2,y_2)=(2,2)). (m=\frac{2 - 10}{2-0}=\frac{-8}{2}=-4). Using the slope - intercept form (y = mx + b) (where (b = 10) when (x = 0)), the equation is (y=-4x + 10).

Step2: Find the equation of the second line

Use the slope formula. Let ((x_1,y_1)=(0,2)) and ((x_2,y_2)=(2,-4)). (m=\frac{-4 - 2}{2-0}=\frac{-6}{2}=-3). Using the slope - intercept form (y=mx + b) (where (b = 2) when (x = 0)), the equation is (y=-3x+2).

Step3: Solve the system of equations

Set (-4x + 10=-3x + 2). Add (4x) to both sides: (10=x + 2). Subtract 2 from both sides: (x = 8). Substitute (x = 8) into (y=-3x + 2): (y=-3\times8+2=-24 + 2=-22).

Answer:

((8,-22))