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

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

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

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.

(-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 )

The addition method is performed over the substitution method in this case because it is easier to eliminate one variable when given two equations. To use the addition method, we first need to choose one variable to eliminate. In this case, we can choose to eliminate either x or y.

Let's choose to eliminate y. To do this, we need to make the coefficients of y in both equations the same or their additive inverses. To achieve this, we can multiply the first equation by 2 and the second equation by 3. This gives us:

Equation 1: 4x - 6y = 20
Equation 2: 15x + 6y = 18

Now, we can add the two equations together:

(4x - 6y) + (15x + 6y) = 20 + 18
19x = 38

Divide both sides of the equation by 19 to solve for x:

x = 38 / 19
x = 2

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

2x - 3y = 10
2(2) - 3y = 10
4 - 3y = 10
-3y = 10 - 4
-3y = 6

Divide both sides of the equation by -3 to solve for y:

y = 6 / -3
y = -2

Therefore, the solution to the system of equations is x = 2 and y = -2.