Question

4x+2y=-3, -5x-3y=5. what is the solution of the system

Answer 1

Have you been specifically told to use either elimination, or substitution to solve this? If you're not sure, you can probably use either, let us know :)

Answer 2

elimination

Answer 3

So you want to change your two equations, so that the coefficient of x or y is the same size, and opposite sign in both cases. To do this, identify the lowest common multiple for each pair of coefficients. For example, the LCM for the coefficients of x is the LCM of 4 and 5, which is 20. That means you need to use arithmetic to change your equations so they have 20x, and -20x. The ys are easier in this case, so let's work with those. The LCM of 2 and 3 is 6, so we want 6y, and -6y. Take the first equation \[4x+2y=-3\] To make sure we have 6y here, we need to multiply EVERYTHING by 3:\[3(4x)+3(2y)=3(-3)\]which gets you \[12x+6y=-9\]that's your new first equation. Try the same thing with the second equation, and get back to us. You want to have a -6y.

Answer 4

what i got was 12x+6y=-9 for the first one and 10x-6y=10 for the second on. the i added them and got 22x=1. after that i got stuck

Answer 5

That's really close. Don't forget that the second equation starts with a -5x, so you'll end up with \[-10x-6y=10\]As you rightly say, add that to the previous equation, you get \[2x=1\]So let me ask you, if 2 tables cost 1 dollar, what does 1 table cost?

Answer 6

50 cents

Answer 7

Exactly, and you presumably got that by dividing by 2. You do the same thing here\[2x=1\]\[\Leftrightarrow \frac{2x}{2}=\frac{1}{2}\rightarrow \text{dividing by 2}\]\[\Leftrightarrow x=\frac{1}{2}\]Now you know what x is, so you can use this information to figure out y Look back at the first equation\[4x+2y=-3\]Since \(x=\frac{1}{2}\), you know that \[4(\frac{1}{2})+2y=-3\]Can you figure out y from there?

Answer 8

i corrected my mistake and got that answer and i know one of the solutions is (1/2) , but i dont understand how to get the other solution

Answer 9

Well now you know what the value of x is, you can substitute it into one of your previous equations\[4x+2y=-3\]becomes \[4(\frac{1}{2})+2y=-3\]where all you do there is replace the x with \(\frac{1}{2}\). So that's just another equation, but it's one you can solve with various tools in your arithmetic and algebraic toolbox.

Answer 10

4(1/2)2y=-3 is where im stuck at . i dont understand how to the the other solution from there. and which tools are they?

Answer 11

correction: 4(1/2)+2y=-3

Answer 12

Well starting from \[4(\frac{1}{2})+2y=-3\], following your order of operations, the first thing you have to do is multiply the 4 and the \(\frac{1}{2}\). \[2+2y=-3\]. Then since you can't do anything further, you have to start doing things to both sides of that equation in the reverse order of operations. First then is add/subtract 2 from both sides:\[2y=-5\], now multiply/divide by 2\[y=\frac{-5}{2}\]

Answer 13

so my final answer would be (1/2, -5/2), . thank you so much im going to copy this into my notes