which ordered pair of numbersis the solution of the following sysytems? 2x + 3y = 12 and 2x - y = 4

Question

a. (2,3) b. (3,2) c, (1,-2) d. (-3,6)

Answer 1

Hi Maddie, 

Step One: We can reach the answer by solving the system of equations:

2x+3y=12

2x-y=4 Multiply both sides by -1:

 

2x+3y=12
-2x+y=-4 Simplify: 2x-2x+3y+y=12-4

 

3y+y=8 Combine like terms

4y=8 Divide both sides by 4

y=2

Step Two: Looking at the answer choices, (2,3) b. (3,2) c, (1,-2) d. (-3,6) only b has y=2. This is the correct answer. 

∴The ordered pair (3,2) is the solution to the system of equations 2x+3y=12 and 2x-y=4

Best, 

Star

2x+3y=12

2x-y=4

Answer 2

Write the equations under each other.  Then subtract

 

2x + 3y = 12

2x -    y = 4

 

 0 + 4y = 8   divide each side by 4

 

         y = 2   plug the 2 in for y in one of the equations and find the x value

 

2x + 3y = 12

2x + 3(2) = 12

 

2x + 6 = 12

 

       -6   -6

 

      2x   = 6

 

         x = 3

 

The correct ordered pair would be (3,2)