4x-4y=8 3x+2y=-9

Question

solving systems using the substitution and addition method

Answer 1

Hi Mercedes--here are the substitution and the addition methods:

 

If you want to use the substitution method, you're solving for one of the variables "in terms of the other" so you can "sub it out" for the other:

 

Take the first equation and divide the whole thing by 4, so you are left with:

 

x - y = 2.  Then you can isolate and solve for x by adding y to both sides, so that x = y + 2.

 

Now wherever you see x, you can put in y + 2 instead.

 

So: 3(y + 2) + 2y = -9, or 3y + 6 + 2y = -9, or 5y + 6 = -9

 

which means that 5y + 15 = 0, so 5y = -15, so y = -3.

 

Remember that y + 2 is x, so that means -3 + 2 = x, so x = -1.

 

Finally, plug those 2 values into either equation (or both!) and make sure they work. (Hint: they do. :-)  )

 

NOW: to solve by the addition method, you stack the 2 equations on top of one another like a giant addition equation, although in this case it will be better to subtract:

 

4x - 4y = 8

-    3x + 2y = -9

_______________

 x  - 6y = 17

 

Then isolate x.  x = 17 + 6y. Now you can sub in 17 + 6y in place of x in the 2 equations and solve them with the same remaining steps as above. You should get the same x and y values as above.

 

Hope this helps!

 

Matt in New York

Answer 2

Subtract 3x from both sides of the second equation.  It now looks like this:  2y=-9-3x.
Then, rewrite the first equation like this:  4x-2(2y)=8.
Next, write -9-3x in the second place, in the parentheses, in place of 2y:  4x-2(-9-3x)=8.
Now you have one equation with one unknown.
Simplify:  4x+18+6x=8.
Again:  10x+18=8
Subtract 18 from both sides:  10x=-10.
Divide both sides by 10:  x=-1.
Substitute this back in instead of x in either equation, solve for y, then check the coordinate pair in both equations.

x=-1, y=-3:  (-1,-3)

:)