Question

Part 1: Solve the system by graphing. Draw the graphs on paper and indicate their intersection point. Type the ordered pair solution here as your answer to Part 1.
Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordered pair.
Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair.

2x+3y=6

x-2y=10

Answer 1

Part (1):
The graph is shown in the attached image.
As we can note from the graph, the solution of the system of equations is indicated by the point of intersection between the two lines which is (6,-2)

Part (2):
The equations given are as follows:
2x + 3y = 6 ...........> equation I
x - 2y = 10
which can be rewritten as:
x = 2y + 10 ...........> equation II

Substitute with equation II in equation I and solve for y as follows:
2x + 3y = 6
2(2y+10) + 3y = 6
4y + 20 + 3y = 6
7y = 6 - 20
7y = -14
y = -2

Substitute with y in equation II to get x as follows:
x = 10 + 2y 
x = 10 + 2(-2)
x = 10 - 4
x = 6

The solution is (6,-2)

Part (3):
The equations given are:
2x + 3y = 6 .............> equation I
x - 2y = 10 ...........> equation II

Multiply equation II by -2, this will give:
-2x + 4y = -20 ............> equation III

Add equation I and equation III as follows:
                                       2x + 3y = 6
                                +    -2x + 4y = -20
                           .........................................
                                       0x + 7y = -14
7y = -14
y = -2

Substitute with y in equation II to get x as follows:
x - 2y = 10
x - 2(-2) = 10
x + 4 = 10
x = 10 - 4
x = 6

The solution is (6,-2)

Hope this helps :)