Solve this system of equations by graphing: 3x - y = 9 and x + y = 7

Question

Solve this system of equations by graphing: 3x - y = 9 and x + y = 7. Clearly state the solution to this system. Explain,  how you graphed your lines, and what the significance of the intersection point is

Answer 1

MAKING A GRAPH HERE WOULD BE DIFFICULT.  I WILL TRY TO EXPLAIN THIS SO YOU CAN GRAPH IT.

 

FIRST SOLVE EACH EQUATION FOR y.

 

3x -  y = 9                                    x + y =  7

 

       -y = 9 - 3x

 

         y = 3x - 9                                  y = 7 - x

 

NOW CREATE ORDERED PAIR TABLES FOR EACH EQUATION.

 

         x          y                                      x        y  

 

         0         -9                                     0        7

 

         1         -6                                     1        6

 

         2         -3                                     2        5

 

         3          0                                     3         4

 

         4          3                                     4         3

 

NOTICE THERE IS A COMMON ORDERED PAIR FOR THESE 2 EQUATIONS.  (4,3)

 

IF YOU PLOTTED THESE POINTS ON A SINGLE GRAPH AND DREW THE LINES, THEY WOULD CROSS AT THE ORDERED PAIR  (4,3).

 

THE LINES WERE GRAPHED BY PLOTTING THEIR ORDERED PAIRS.

 

THE SIGNIFICANCE OF THE INTERSECTION POINT IS THAT THE POINT (4,3) IS THE ONLY POINT WHERE x AND y WILL WORK IN BOTH EQUATIONS.