solve the system of equations by graphing

Question

solve the system of equations by graphing

-2x-y=-6

5x+y=9

 

what is the solution of the system of equations. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

 

a)__ (type an ordered pair)

b) the system of equations has infinitely many solutions

c) the system of equations has no solution

Answer 1

-2x-y=-6

 5x+y=9

 

 Solving the equations by graphing only is the most difficult method, but it is important that students ALWAYS realize  exactly what is meant graphically by any algebraic skill.

 

 Graphing both equations requires rewriting the equations using the standard form y=mx +b 

 

 -2x + 6 = y is a line with slope m=-2 and y-intercept y=6, or (0,6)

 

   y = -5x + 9 is a line with slope m=-5 and y-intercept y=9, or (0,9)

 

   Since the slopes are different, the two lines are not parallel, so the answer cannot be (c)

   Since the y-intercepts are different, the lines do not lie on top of each other, so the answer cannot be (b)

 

   It's necessary to graph both lines and find the ordered pair where they cross each other.

 

   For each point, we have found one ordered pair, but we need one more for each line to graph them.

   The x-intercept is an easy point to find (where y=0). Substitute in 0 for y in both equations.

 

   -2x+6=0 has a solution of -2x=-6 or x=3. The x-intercept is (3,0). The y-intercept was (0,6)

      This line can be plotted by plotting those two ordered pairs and drawing a line through them with a ruler, etc.

 

   -5x +9=0 has a solution of -5x = -9 or x= 9/5 = 1.8. The x-intercept is (1.8, 0). The y-intercept was (0,9).

      Now Plot and draw the line as above.

 

   The ordered pair of the solution is found at the one point where the two lines cross :)

 

   What result did you find?