solve the following system of equations graphically on the set of axes below.\n\n$y = 2x - 2$\n\n$2x + 3y =…

solve the following system of equations graphically on the set of axes below.\n\n$y = 2x - 2$\n\n$2x + 3y = 18$\n\nplot two lines by clicking the graph.\nclick a line to delete it.

solve the following system of equations graphically on the set of axes below.\n\n$y = 2x - 2$\n\n$2x + 3y = 18$\n\nplot two lines by clicking the graph.\nclick a line to delete it.

Answer

Explanation:

Step1: Find two points for (y = 2x-2)

  • When (x = 0), (y=2\times0 - 2=-2). So one point is ((0,-2)).
  • When (y = 0), (0 = 2x-2), then (2x=2), (x = 1). So another point is ((1,0)).

Step2: Rewrite (2x + 3y=18) in slope - intercept form

Solve (2x + 3y=18) for (y): [ \begin{align*} 3y&=-2x + 18\ y&=-\frac{2}{3}x+6 \end{align*} ]

  • When (x = 0), (y=-\frac{2}{3}\times0 + 6=6). So one point is ((0,6)).
  • When (y = 0), (0=-\frac{2}{3}x + 6), then (\frac{2}{3}x=6), (x = 9). So another point is ((9,0)).

Step3: Solve the system of equations algebraically (to confirm the intersection point)

Substitute (y = 2x-2) into (2x+3y = 18): [ \begin{align*} 2x+3(2x - 2)&=18\ 2x+6x-6&=18\ 8x&=18 + 6\ 8x&=24\ x&=3 \end{align*} ] Substitute (x = 3) into (y = 2x-2), (y=2\times3-2=4).

Answer:

The solution of the system of equations is ((3,4))