## itsjustme_lol 2 years ago Explain, in complete sentences, how you would use the substitution method to solve the following system of equations.

1. itsjustme_lol

2x – y = 5 x + 2y = 15

2. Aylin

Are you familiar with the substitution method?

3. itsjustme_lol

sorta, not very good in math

4. AWarn

Solve either of the equation for x and then substitute that value for x into the other equation.

5. AWarn

Take the second equation and solve for x: x=15-2y then substitute this into the first equation. You get 2*(15-2y)-y=5 then solve for y.

6. Aylin

Ok. I'm not going to give you the specifics for your problem, but I can tell you what to do generally. When you have a system of equations, in order to solve via the substitution method you first isolate one of the variables in one equation. So for example if you had this as a system:$ax+by=c$$dx+ey=f$we could start by isolating x in the first equation:$x=\frac{ by }{ a }+\frac{ c }{ a }$Then you just take that and plug it into x in the other equation:$d \times (\frac{ by }{ a }+\frac{ c }{ a })+ey=f$And then you just solve that equation for y. And then once you know what y, you just plug that back into $x=\frac{ by }{ a }+\frac{ c }{ a }$and that gives you x also. Does that make sense?

7. itsjustme_lol

thats still confusing..:( im sorry..

8. Aylin

That's ok. How 'bout I show you an example that's similar to your problem?

9. itsjustme_lol

that might help

10. ktnguyen1

Solve for y in the 1st equation and plug y value in the 2nd equation. Or, solve for x in the 2nd one and plug that x value in the 1st.

11. Aylin

So say we have the following system:$3x-y=7$$x+4y=1$So the first step is to isolate one of the variables in one of the equations. I'm going to choose to isolate y in the first equation, since that looks easy. So now I would write:$3x-3x-y=7-3x$$-1 \times (-y)= -1 \times (7-3x)$$y=3x-7$In a sentence, I would say that I chose the first equation, subtracted 3x from both sides of the equal sign, and then multiplied both sides by -1. Then in the second equation instead of y, I would substitute in this new value we found for y:$x+4(3x-7)=1$$x+12x-28=1$$13x-28+28=1+28$$13x=29$$x=\frac{ 29 }{ 13 }$Again in a sentence I would say that I substituted the value of y I found using the first equation into the second equation and then expanded, which resulted in x+12x-28=1. Then I would say that I added 28 to both sides and then divided by 13 in order to find x. So now we know what x is, but what is y? Well, remember that equation we found for y in terms of x earlier? We just plug our x value into it and that will give us y, like so:$y=3(\frac{ 29 }{ 13 })-7$$y=\frac{ 87 }{ 13 }-\frac{ 91 }{ 13 }$$y=\frac{ -4 }{ 13 }$ Does that clear it up for you?

12. itsjustme_lol

Yes, Thankyou!!