Explain why the addition method might be preformed over the substitution method for solving the system

Question

2x – 3y = 10
5x + 2y = 6
What is the solution of this system?

Answer 1

2 x – 3 y = 10 Multiply both sides by 2

4 x - 6 y = 20

5 x + 2 y = 6 Multiply both sides by 3

15 x + 6 y = 18

4 x - 6 y = 20

+

15 x + 6 y = 18

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4 x + 15 x - 6 y + 6 y = 20 + 18

19 x = 38 Divide both sides by 19

x = 38 / 19

x = 2

To get the value of y you need to use the substitution method.

Substitute x = 2

into equation

2 x - 3 y = 10

2 * 2 - 3 y = 10

4 - 3 y = 10

- 3 y = 10 - 4

- 3 y = 6 Divide both sides by - 3

y = 6 / - 3

y = - 2

Answer 2

The point of intersection of the graphs of the equations of the system

Ax – 4y = 9
4x + By = –1

is (–1, –3). Explain how to find the values of A and B, then find these values.

Answer 3

(-1 , -3) = ( x,y)

put the X and Y values into the first equation,

Ax-4y=9

A(-1)- 4(-3)= 9

-A + 12=9

-A=-3

A= 3 [ Multiply by (-1)]

Now put the X and Y values to the second equation,

4( -1) +B( -3) =-1

-4- 3B=-1

-3B= 3

B=-1 [ Multiply by negative (-1)]

Just check are those ans is right, put the all values to the equation......

3(-1)-4(-3)=9

9=9

And, 4(-1)+(-1)(-3)=-1

-4 + 3=-1

-1 = -1

So, (A,B)= ( 3, -1 )