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Let's write our 2 original equations. \(x + 3y = 5\) Eq. 1 \(7x - 8y = 6\) Eq. 2
The problem is asking for a new system of equations which is obtained by keeping equation 2 unchanged, and equation 1 is replaced by the sum of equation 1 and a multiple of equation 2. The new system of equations will be: \(x + 3y = 5\) Eq. 1 kept unchanged \(\_\_\_\_\_\_\_\_\_\_\) A new equation replacing Eq. 2
Now we need to read in the problem what the new equation that replaces equation 2 is. "If equation 2 is multiplied by 1, ..." We are told that equation 2 is multiplied by 1. We already were told that we needed to add a multiple of equation 2 to equation 1. Now we know that the multiple of equation 2 is obtained by multiplying equation 2 by 1. What is equation 2 (below) multiplied by 1 on both sides? \(7x - 8y = 6\) Eq. 2
can you try it out? :) we can't do it for u
@dom4958 Are you there?
@dom4958 then try it out
well if I'm multiplying equation 2 by 1 it would still be the same wouldn't it? or would the - sign change next to 8y?
Ok. What is any number multiplied by 1? What is 2 * 1 = 3 * 1 = pi * 1 = What does multiplying by 1 do to a number?
@mathstudent55 nothing. it stays the same
Exactly. Multiplying by 1 does not change a number, so multiplying a whole equation by 1 does not change the equation.
That means when we multiply the second equation by 1, we end up with the second equation, just as it was originally.
\(7x - 8y = 6\) Eq. 2 multiplied by 1
Now we add Eq. 1 to Eq. 2 multiplied by 1: \(~~~~~~~~x + 3y = 5\) Eq. 1 \(+~~~7x - 8y = 6\) Eq. 2 multiplied by 1 \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Do you know how to add the equations in the response above?
Add like terms that are placed one above the other. What is x + 7x = ?
i think he's afk just waiting for the answer
sorry I'm back, give me a moment to read what you just said
would this be correct or am i off track? x+3y=5 + 7x−8y=6 ______________ 8x - 5y =11???
Now you replace equation 1 by this new equation, and equation 2 remains the same as it was. What is the new system of equations?
8x - 5y =11 Eq.1 7x−8y=6 Eq.2
Original system New system \(x+3y=5\) Eq. 1 ---replaced by---> \(8x - 5y = 11\) \(7x−8y=6\) Eq. 2 ---remains as----> \(7x - 8y = 6\)
Exactly. Now read the choices and choose the correct one.
B thank you so much. you made it really clear i appreciate it
Great. You're welcome. Notice that you did all the work. I just guided you through it. When you have a problem like this one, break down the instructions into small steps and do one step at a time until you get it all done. Good job!
@mathstudent55 thanks, i honestly have no idea how people can memorize this. I'm good at every other subject but math just gets me lol
Each of us has our strong and weak subjects. This way we can help each other.