1) x+2y=7, 2x-y=4
What I did:
multiply 2x-y=4 by -2 so I could eliminate the y variable.
-4x-2y = -8
+ x +2y =7
= -3x =-1
Divided -1 by =1 and got x=1/3
I only need someone to check my answer. Also one last question, can I use the elimination method for all system of equations or will there be a time when I absolutely have to use the substitution method?
but go back and get y from either
x+2y=7, 2x-y=4
1/3 + 2 y = 7
2 y = 20/3
y = 10/3
or
2(1/3) -y = 4
y = 2/3 - 4 NOPE so wrong !!!!
I will try it
x+2y=7, 2x-y=4
x + 2 y = 7
-4 x + 2 y = -8
-------------------- subtract
5 x = 15
x = 3 (Not what you had)
back for y
3 +2 y = 7
2 y = 4
y = 2
-------------------------
NOW CHECK THAT
x + 2 y = 7 ?
3 + 4 = 7 YES !
2 x - y = 4 ?
6 - 2 = 4 YES
so I got it right.
error in -4x-2y = -8
you multiplied by -2 so it should have been
-4x+2y = -8 , and you would now have to subtract the two equations
-4x + 2y = -8
x + 2y = 7
-5x = -15
x = 3
you did not find the y
in our case , sub x = 3 into
x+2y = 7
3 + 2y = 7
2y = 4
y = 2
so x = 3, y = 2
Elimination does work all the time, in many cases you will have to perform
some operations on either one or even both equations.
You will have to judge if one method is better than another.
I look at the coefficients of both equations . If I see an x or y term with 1 as coefficient, I might choose substitution.
e.g. in your case one equation is x+2y=7
I would change that to x = 7-2y and sub that into the 2nd
2x-y=4
2(7-2y) - y = 4
14 - 4y - y = 4
-5y = -10
y = 2, then in x = 7-2y , x = 7-4 = 3 , same as above
To solve the system of equations:
1) x + 2y = 7
2) 2x - y = 4
Your steps are correct until you simplified the equations. However, there seems to be a mistake when you added the two equations. The correct equation should be:
-4x - 2y = -8
+ (x + 2y) = 7
---------------
-3x = -1
Now, when you divide both sides of the equation -3x = -1 by -3, you will get x = 1/3. So, your answer for x is indeed correct.
To find the value of y, substitute x = 1/3 into either of the original equations. Let's use the first equation:
x + 2y = 7
1/3 + 2y = 7
2y = 7 - 1/3
2y = 21/3 - 1/3
2y = 20/3
y = 20/6
y = 10/3
Therefore, the solution to the system of equations is x = 1/3 and y = 10/3.
Regarding your second question, the elimination method can be used for most systems of equations, especially when the coefficients of one variable in both equations can be easily multiplied to make them cancel each other out. However, there may be situations where the substitution method is more convenient or simpler to use. It depends on the specific system of equations and the individual's preference or strategy. Both methods are valid and can be applied to various scenarios.