solve the following system of equations graphically on the set of axes below.\n$y = \\frac{2}{3}x - 7$\n$y =…

solve the following system of equations graphically on the set of axes below.\n$y = \\frac{2}{3}x - 7$\n$y = -\\frac{1}{3}x - 4$\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$y = \\frac{2}{3}x - 7$\n$y = -\\frac{1}{3}x - 4$\nplot two lines by clicking the graph.\nclick a line to delete it.

Answer

Answer:

The solution to the system of equations is ( x = 3 ), ( y = -5 ) (or the point ((3, -5))).

Explanation:

Step 1: Analyze the first equation ( y = \frac{2}{3}x - 7 )

To graph this line, we can find two points.

  • When ( x = 0 ), ( y = \frac{2}{3}(0) - 7 = -7 ). So one point is ( (0, -7) ).
  • When ( x = 3 ), ( y = \frac{2}{3}(3) - 7 = 2 - 7 = -5 ). So another point is ( (3, -5) ).

Step 2: Analyze the second equation ( y = -\frac{1}{3}x - 4 )

To graph this line, we find two points.

  • When ( x = 0 ), ( y = -\frac{1}{3}(0) - 4 = -4 ). So one point is ( (0, -4) ).
  • When ( x = 3 ), ( y = -\frac{1}{3}(3) - 4 = -1 - 4 = -5 ). So another point is ( (3, -5) ).

Step 3: Find the intersection point

The two lines intersect where they have the same ( x ) and ( y ) values. From the points we calculated, both lines pass through ( (3, -5) ). This is the solution to the system of equations.