Question 21018: in class we're learning about system of equations and i don't really understand it so what is the coordinate for x-4y=15 and 2x+5y=4. could you explain it?
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
Off the top of my head, I can think of five different ways to solve this problem. I don't know which method(s) you've studied, so I have to guess.
I'll use the "substitution method".
The strategy in this method is to solve one of the equations for one of the variables. You'll end up with an expression that contains the other variable.
Substitute this expression into the other equation, and that will give you an equation that contains only one variable. Solve it in the normal way.
Once you have the value of that variable, substitute it into the expression you got from solving the first equation.
Here goes:
I choose to solve the first equation for 'y'.
x - 4*y = 15
-4*y = 15 - x
y = (15 - x)/(-4)
Now I substitute this expression for y in the second equation.
2*x + 5*y = 4
2*x + 5 = 4
I'll clear the fraction by multiplying both sides by -4.
-8*x + 5*(15 - x) = -16
-8*x + 75 - 5*x = -16
-13*x = -91
x = -91/(-13)
x = 7
Now that we know x is 7, we substitute it for x in our formula for y above.
y = (15 - x)/(-4)
y = (15 - 7)/(-4)
y = 8/(-4)
y = -2
The solution is x = 7 and y = -2.
You can verify this solution by substituting 7 for x and -2 for y into both of the original equations to see that it yields true statements.
~ Mark
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