1.What is the value of x-y if 5x-3y=3 and
-x+3y=9 ?
2.Rewrite -2x^-1 /x^2y^-1 with positive
exponents
3. What is the value of xy if x+5y=26 and
-x+y=4 ?
#1 and #3 are the same type of problem.
Solve the two equations, once you have the x and y, just perform the required arithmetic.
I will do the first you do #3
add the equations:
4x = 12
x = 3
sub back into the 2nd (looks easier)
-3 + 3y = 9
3y = 12
y = 4
so x=3, and y = 4, then
x-y = 3-4
= -1
#2
I will assume you mean
-2x^-1 /(x^2y^-1)
= (-2/x)(1/x^2)(1/y)
= -2/(x^3 y)
Yes,but is that the answer to#2, because the multiple choice answers are:A.-2x^3y
B.2x^3/y C. -2y/x^3 D.-2y/x E.2y/x
Which one is it,please help me Reiny.
1. To solve for the value of x-y, we need to solve the given system of equations:
Given equations:
5x - 3y = 3 ........(1)
-x + 3y = 9 ........(2)
First, let's eliminate one variable by adding these two equations together:
(5x - 3y) + (-x + 3y) = (3 + 9)
This simplifies to:
4x = 12
Now, we can solve for x by dividing both sides of the equation by 4:
x = 3
Next, substitute the value of x back into one of the original equations to solve for y. Let's use equation (2):
-x + 3y = 9
Substituting x = 3, we get:
-3 + 3y = 9
Next, isolate y by adding 3 to both sides:
3y = 12
Finally, solve for y by dividing both sides by 3:
y = 4
Now that we have the values of x and y, we can find x - y:
x - y = 3 - 4 = -1
Therefore, the value of x - y is -1.
2. To rewrite -2x^-1 / x^2y^-1 with positive exponents, we can use the rules of exponents:
-2x^-1 / x^2y^-1 can be simplified as follows:
-2 / (x^(-1 + 2) * y^(-1))
Simplifying the exponents:
-2 / (x^(1) * y^(-1))
Now, move the y term from the denominator to the numerator by changing its exponent to positive:
-2y / x^1
Finally, since x^1 is equal to x, we can write the expression as:
-2y / x
So, the rewritten expression with positive exponents is -2y / x.
3. To find the value of xy, we need to solve the given system of equations:
Given equations:
x + 5y = 26 ........(1)
-x + y = 4 ........(2)
First, let's eliminate one variable by adding these two equations together:
(x + 5y) + (-x + y) = (26 + 4)
This simplifies to:
6y = 30
Now, we can solve for y by dividing both sides of the equation by 6:
y = 5
Next, substitute the value of y back into one of the original equations to solve for x. Let's use equation (2):
-x + y = 4
Substituting y = 5, we get:
-x + 5 = 4
Next, isolate x by subtracting 5 from both sides:
-x = -1
Finally, solve for x by multiplying both sides by -1:
x = 1
Now that we have the values of x and y, we can find xy:
xy = 1 * 5 = 5
Therefore, the value of xy is 5.