Question

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Given the system of linear equations:

{y= -5 y=3x -2



Part A: Graph the system of linear equations.

Part B: Use the graph created in Part A to determine the solution to the system.

Part C: Algebraically verify the solution from Part B.

Answer 1

QUESTION 1

the solution is (-1,-5)

To verify the solution algebraically, we need to multiply the first equation with -1 and then sum them up

-y=5

y=3x-2

0=3x+3

3x=-3

x=-3/3

x=-1

Then, we use this value to find the other one

y=3x-2

y=3(-1)-2

y=-3-2

y=-5

Therefore, the solution is (-1,-5), which is the same showed graphically.

QUESTION 2.

Using the same process as we did in the QUESTION 1. The image attached shows both lines and the interception point which is the solution. So, the solution is (6,0).

To verify the solution algebraically, we must multiply the second equation by -6

x+6y=6

-6y=-2x+12

x=-2x+18

x+2x=18

x=18/3

x=6

Then, we use this value to find the other one

x+6y=6

6+6y=6

6y=6-6

y=0/6

y=6

Therefore, the solution is (6,0),