Answer:
First equation: y = -2x
Second equation: y = 3 - x
Solution: (1, -2)
Step-by-step explanation:
Assuming the ordered pairs of the tables are:
Table 1
(-5, 10) (-1, 2) (0, 0) (11, -22)
Table 2
(-8, -11) (-2, -5) (1, -2) (7, 4)
To create a linear equation, pick 2 ordered pairs. Calculate the slope by using the slope formula, then use the points-slope form of the linear equation to form the equation.
[tex]\textsf{slope }m=\dfrac{\textsf{change in }y}{\textsf{change in }x}[/tex]
[tex]\textsf{point-slope form : }y-y_1=m(x-x_1)[/tex]
Equation 1
[tex]\textsf{slope }m=\dfrac{2-10}{-1+5}=-2[/tex]
[tex]y-0=-2(x-0)\\\\\implies y=-2x[/tex]
Equation 2
[tex]\textsf{slope }m=\dfrac{-5+11}{-2+8}=1[/tex]
[tex]y+11=1(x+8)\\\\\implies y=x-3[/tex]
Solution to the System
Equate the equations and solve for x:
-2x = x - 3
⇒ 0 = 3x - 3
⇒ 3x = 3
⇒ x = 1
Substitute found value of x into one of the equations and solve for y:
y = 1 - 3 = -2
Therefore, the solution is (1, -2)
