Question

elect the correct answer from each drop-down menu. A system of linear equations is given by the tables. x y -5 10 -1 2 0 0 11 -22 x y -8 -11 -2 -5 1 -2 7 4 The first equation of this system is y = x. The second equation of this system is y = x − . The solution to the system is ( , ).

Answer 1

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.

$\textsf{slope }m=\dfrac{\textsf{change in }y}{\textsf{change in }x}$

$\textsf{point-slope form : }y-y_1=m(x-x_1)$

Equation 1

$\textsf{slope }m=\dfrac{2-10}{-1+5}=-2$

$y-0=-2(x-0)\\\\\implies y=-2x$

Equation 2

$\textsf{slope }m=\dfrac{-5+11}{-2+8}=1$

$y+11=1(x+8)\\\\\implies y=x-3$

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)