Question

Consider the following three systems of linear equations. System A System B System C -5x - 4y = 9 [A1] 13x = 39 [81] x=3 [C1] 9x + 2y = 15 [42] 9x + 2y = 15 [B2] 9x+2y = 15 (C2] Answer the questions below. For each, choose the transformation and then fill in the blank with the correct number, The arrow (+) means the expression on the left becomes the expression on the right. How do we transform System A into System B?

Answer 1

multiplying A1 by 0 and adding it to A2, we will get B2

multiplying [A2] by 1, we get [B2]

multiplying A2 by 2 and adding it to A1, we get B1

Here, we want to understand how we can transform the equations to one another

Firstly, we want to know what will make equation [A1] tranform into [B1]

From the image;

[A1] is -5x-4y = 9

B1 is 13x = 39

There is no way to multiply a number by A1 to give B1

Secondly, we want to transform [A2] to [B2]

[A2] is 9x + 2y = 15

[B2] is 9x + 2y = 15

We can see that both are the same thing

So by multiplying [A2] by 1, we get [B2]

So, what we fill in the blank would be 1

Thirdly;

we want to get [B2] from [A1] and [A2] addition

B2 is 9x+2y = 15

A1 is -5x-4y = 9

A2 is 9x + 2y = 15

So, by multiplying A1 by 0 and adding it to A2, we will get B2

For the fourth;

We want to get B1 from A2 and A1

B1 is 13x = 39

A2 is 9x + 2y = 15

A1 is -5x-4y= 9

So by multiplying A2 by 2 and adding it to A1, we get B1

Mathematically, that would be;

2(9x+2y=15) + (-5x-4y=9)

18x+ 4y = 30 + -5x-4y=9

That would give 13x = 39 which is B2