Need help applying substition/addition method to linear equations

Question

I'm having a very difficult time solving these equations. For some odd reason I keep getting a graph answer. For example, when I try to solve 3x + 2y = 14; it keeps telling me the answer is, m=−32,b=7 where m is the slope and b is the y-intercept. Which doesn't make sense to me since I have to apply the addition method which I did.

If anyone could help me figure out what I did wrong, so I could go from there, that would be great.

I need to Apply Substitution Method For:
x+2y=4
2x−y=–7
And I also need to Apply Addition (Elimination) Method For:
3x+2y=14
5x–2y=18

Answer 1

Stacy,

       The substitution method; first you solve one of the equations for one of the variables in term of the other variable. Which one you choose does not matter.

 

x+2y=4

2x-y=-7

 

Let's solve the second equation for y, y=2x+7 now you SUBSTITUTE this expression for y in the first equation

x+2(2x+7)=4, simplifying gives 5x=-10 or x=-2. To find y put x=-2 in either equation and solve for y use equation 1 and -2+2y=4 and solving for y gives y=3 so x=-2, y=3 is the solution.

      If you graphed each of the above lines on the same graph you would find that x=-2, y=3 is the point where the two lines intersect.

 

      To do the addition (elimination) method observe if you ADD the two equations you get 8x=32 or x=4 put this value in either equation and get y=1.

 

 

Hope this helps

 

Jim