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2 years ago

Given the system of equations, what is the solution?5x - 4y = 7x = 5 - 3/2y

Mathematics

1 answer:

nignag [31]2 years ago

8 0

9514 1404 393

Answer:

(x, y) = (61/23, 36/23)

Step-by-step explanation:

We assume you intend the equations to be ...

5x -4y = 7
x = 5 -3/2y

Then in general form, they are ...

5x -4y -7 = 0

2x +3y -10 = 0

The solution using the "cross multiplication method" is ...

1/(15 +8) = x/(40+21) = y/(-14 +50)

(x, y) = (61/23, 36/23)

_____

Comment on "cross multiplication method"

When the coefficients from the general form equations are written as a 2×4 array with the first and last columns the same ...

$\left\{\begin{array}{cccc}5&-4&-7&5\\2&3&-10&2\end{array}\right\}$

the solution is 1/d1 = x/d2 = y/d3, where d1, d2, d3 are the determinants of successive pairs of columns.

d1 = (5)(3) -(2)(-4)
d2 = (-4)(-10) -(3)(-7)
d3 = (-7)(2) -(-10)(5)

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Select the lengths in centimeters that would form a right triangle

Ivenika [448]

Answer:

9, 40 and 41

Step-by-step explanation:

All right triangle have lengths that follow the Pythagorean Theorem (a²+b² = c²). Right triangles have one angle equal to 90°. The two shorter sides form the right angle and the side opposite the right angle is called the hypotenuse.

Using the lengths given, we can use guess and check to see what sum of two sides squared would equal a third side, or just plug them into the equation: a²+b² = c² and see what lengths fit this equation.

I recommend starting with squares you are familiar with:

9² + 40²= 81 + 1600 = 1681

Now, take the √1681 to find the length of 'c', or the hypotenuse:

√1681 = 41

Since these three lengths fit the Pythagorean Theoreom, the would form a right triangle.

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2 years ago

Solve the systems using substitution. − 2x − 5y = − 5 x = 5y − 20

Law Incorporation [45]

-2(5y-20) - 5y = -5
-10y + 40 - 5y = -5
-15y + 40 = -5
-15y = -45, y = 3
x = 5(3) - 20
x = 15 - 20, x = -5
Solution: x = -5, y = 3... or (-5,3)

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2 years ago

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charle [14.2K]

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Anna35 [415]

Answer:

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Step-by-step explanation:

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