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3 years ago

Solve the systems of equations using substitution. 2x+3y=-8 ,x=4y+7

Mathematics

1 answer:

Viktor [21]3 years ago

7 0

Answer:

(-1, -2)

Step-by-step explanation:

Since the question requires the use of substitution, that's how I will go about this.

Logically, since we know what x equals, with respect to y, we can plug that into the other equation for x, making our equation only have y, therefore, we can solve for one variable at a time, and then use that y value to solve for x

2x + 3y = -8

In this case we are told that x = 4y + 7, therefore that's what we substitute in.

2(4y + 7) + 3y = -8

8y + 14 + 3y = -8

11y +14 = -8

11y = -22

y = -2

Now, since we know y's exact value, we can use that and solve for x in the other equation.

x = 4(-2) + 7

x = -8 + 7

x = -1

Therefore, your final answer is

(-1, -2)

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Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'

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Scale factor is a ratio. The correct option is C.

<h3>How are scale drawings formed?</h3>

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

$\rm 1\: ft : \dfrac{s}{k}\: in.$

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

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2 years ago

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Answer:

Step-by-step explanation:

Even though the triangle is "upside down"

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3 years ago

What is an equation in point-slope form for the line perpendicular to y = 7x + 14 that contains (3, –7)?

umka21 [38]

The equation of the perpendicular line is y + 7 = -1/7(x - 3)

<h3>How to determine the line equation?</h3>

The equation is given as

y = 7x + 14

Also, from the question

The point is given as

Point = (3, -7)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 7

This means that the slope of y = 7x + 14 is 7

So, we have

m = 7

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/7

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = -1/7

(x₁, y₁) = (3, -7)

So, we have

y = -1/7(x - 3) - 7

Evaluate

y = -1/7(x - 3) - 7

Add 7 to both sides

y + 7 = -1/7(x - 3)

Hence, the perpendicular line has an equation of y + 7 = -1/7(x - 3)