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Aleks [24]
3 years ago
11

Use the substitution method to solve the given system of equations. Write your answer as an ordered pair, (x, y).

Mathematics
2 answers:
Lorico [155]3 years ago
4 0

2x - 2y = -2

x - 4y = 5

In x -4y =5, add 4y to both sides to get x = 4y +5

Now substitute that equation for x in the first equation:

2x - 2y = -2

2(4y +5) - 2y = -2

Simplify:

8y +10 - 2y = -2

Combine like terms:

6y +10 = -2

Subtract 10 from both sides:

6y = -12

Divide both sides by 6:

y = -12 /6

y = -2

Now you have y, substitute y in the second equation to solve for x:

x - 4y = 5

x -4(-2) = 5

Simplify:

x+8 = 5

Subtract 8 from both sides:

x = -3

Now you have x = -3 and y = -2

The answer is (-3,-2)

Gnoma [55]3 years ago
3 0

Answer:

(-3, -2)

Step-by-step explanation:

Look at the second equation, we can easily rearrange it to make x the subject.

x - 4y = 5

x = 4y + 5

Now lets put that into the second equation

2x - 2y = -2

2(4y + 5) - 2y = -2

6y + 10 = -2

6y = -12

y = -2

Now lets find x!

x = 4y + 5

x = 4(-2) + 5

x = -3

Now lets format the answer like the question says (ordered pair)

(-3, -2)

Recap: We used substitution and made an equation to work out one of the variables first, then found the second variable using the first.

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Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

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