SOLUTION: I have just started on equation substitutions. They are very confusing, and my entire 10th grade class is struggling. can you help me solve this substitution?
4x+y=-2 2x=-y
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Question 120298: I have just started on equation substitutions. They are very confusing, and my entire 10th grade class is struggling. can you help me solve this substitution?
4x+y=-2 2x=-y
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4x+y=-2 2x=-y
-------------
Solve the "simpler" equation for "y":
y = -2x
Substitute that value of "y" in the other equation to solve for "x":
4x+(-2x)= 2
4x-2x = 2
2x = 2
x = 1
----------
Substitute that into y = -2x to solve for "y":
y = -2*1 = -2
------------------
The solution for the system is (1,-2)
==================================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's solve the second equation for y
Start with the second equation
Divide both sides by -1 to isolate y
Divide
So our second equation is now:
Which means we have the system
Start with the given system
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Multiply
Combine like terms on the left side
Divide both sides by 2 to isolate x
Divide
Now that we know that , we can plug this into to find
Substitute for each
Simplify
So our answer is and which also looks like )
Notice if we graph the two equations, we can see that their intersection is at (-1,2). So this verifies our answer.
Graph of (red) and (green)
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