-3x-y=9 2x+y=6
-x-2y=0 3x+y=0
tell me how to do one and i will try to do the other one..(use the substitutional method)
i mean:
3x-y=9 2x+y=6
x-2y=0 3x+y=0
3x-y=9 2x+y=6
I assume that is one question.
The easiest thing to get by itself is "y" in the 2nd part. If I have 2 xylophones and one Yankee, the way to get the Yankee by himself is to simply take away the 2 xylophones.
2x+y=6
y=6-2x
Now we know what the "yankee" is. He is 6 minus 2 xylophones.
Let's look at the other equation.
3x-y=9
3 xylophones minus the yankee equals nine.
So 3 xylophones minus (6 minus 2 xylophones) equals 9.
3x- (6-2x) = 9
3x - 6 + 2x = 9
Let's add the xylophones together.
5x - 6 = 9
Put the 5 xylophones by themselves. Easiest way is to add the -6 and 6.
5x = 15
If 5 xylophones are worth 15 dollars, how much is one worth?
15 divided by 5 is 3.
A xylophone is worth $3.
How much is the Yankee worth?
3x-y=9
We have 3 xylophones and they are worth $3. 3x3 = 9.
$9 minus the price of the yankee is ... Well ... $9 according to this.
9-y = 9
The yankee must obviously be worth nothing.
Y=0
X=3
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Sure! I will explain how to solve the first set of equations using the substitution method.
The first step is to choose one of the equations and solve it for one variable in terms of the other variable. Let's choose the second equation, 2x + y = 6, and solve it for y.
2x + y = 6
y = 6 - 2x
Now we have an expression for y in terms of x.
The next step is to substitute this expression for y into the other equation. Let's substitute y = 6 - 2x into the first equation, -3x - y = 9.
-3x - (6 - 2x) = 9
-3x - 6 + 2x = 9
-3x + 2x = 9 + 6
-x = 15
x = -15
Once we have the value of x, we can substitute it back into one of the original equations to solve for y.
Using the second equation, 2x + y = 6:
2(-15) + y = 6
-30 + y = 6
y = 6 + 30
y = 36
So the solution to the first set of equations is x = -15 and y = 36.
Now, I will let you try to solve the second set of equations using the substitution method. The equations are:
-x - 2y = 0
3x + y = 0
Start by choosing one equation and solve it for one variable in terms of the other variable. Then substitute this expression into the other equation and solve for the remaining variable. Feel free to ask for further guidance if needed.