Solve the following system of equations using the substitution method 5x+3y=1 X+2y=3

Mathematics

2 answers:

DedPeter [7]3 years ago

4 0

Answer:

(x, y) = (-1, 2)

Step-by-step explanation:

Substitution is easier if you already have an expression for the variable you want to make a substitution for. Here, we don't have that, but we have an equation with x having a coefficient of 1. We can use that to write an expression for x:

x = 3 -2y . . . . . subtract 2y from both sides of the second equation

5(3 -2y) +3y = 1 . . . . substitute for x in the first equation

15 -10y +3y = 1 . . . . . eliminate parentheses

-7y = -14 . . . . . . . . . . subtract 15, collect terms

y = 2 . . . . . . . . . . . . . divide by -7

Use this value in the equation for x:

x = 3 -2(2) = -1

The solution is (x, y) = (-1, 2).

max2010maxim [7]3 years ago

3 0

Answer:

x= -1

y= 2

Step-by-step explanation:

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Given f(x) = 4x^4 find f^-1(x) Then state whether f^-1(x) is a function.

sdas [7]

Answer:

$f^{-1}(x)=\pm\sqrt[4]{\dfrac{x}{4}}$
$f^{-1}(x) \quad\text{is not a function}$

Step-by-step explanation:

To find the inverse function, solve for y:

$x=f(y)\\\\x=4y^4\\\\\dfrac{x}{4}=y^4\\\\\pm\sqrt[4]{\dfrac{x}{4}}=y\\\\f^{-1}(x)=\pm\sqrt[4]{\dfrac{x}{4}}$

f(x) is an even function, so f(-x) = f(x). Then the inverse relation is double-valued: for any given y, there can be either of two x-values that will give that result.

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A function is single-valued. That means any given domain value maps to exactly one range value. The test of this is the "vertical line test." If a vertical line intersects the graph in more than one point, then that x-value maps to more than one y-value.

The horizontal line test is similar. It is used to determine whether a function has an inverse function. If a horizontal line intersects the graph in more than one place, the inverse relation is not a function.

Since the inverse relation for the given f(x) maps every x to two y-values, it is not a function. You can also tell this by the fact that f(x) is an even function, so does not pass the horizontal line test. When f(x) doesn't pass the horizontal line test, f^-1(x) cannot pass the vertical line test.

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The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.