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2 years ago

Given the equation 8x + 4y = 2, a second equation that forms a system with no solution is:

Mathematics

1 answer:

Murrr4er [49]2 years ago

4 0

Answer:

4x + 2y = 2

Step-by-step explanation:

8x + 4y = 2 ( divide each term by 2 )

4x + 2y = 1 → (1)

we require a situation where the left side cannot possibly equal the right side.

using 4x + 2y = 2 → (2)

subtract (1) from (2) term by term

(4x - 4x) + (2y - 2y) = 2 - 1 , that is

0 + 0 = 1

0 = 1 ← not possible

thus the system has no solution

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Please help. 100 points to best answer!!!

Irina-Kira [14]

1. The slope of a line that is perpendicular to a line whose equation

is 5y = 10 + 2x is $\frac{-5}{2}$

The line y = 2x - 1 is neither parallel nor perpendicular to the line

y = -2x + 3

The line y = -2x + 5 is parallel to the line y = -2x + 3

The line y = $\frac{1}{2}$ x + 7 is perpendicular to the line

y = -2x + 3

3. The equation of the line that passes through the point (5 , -4) and

is parallel to the line whose equation is 2x + 5y = 10 is

y = $\frac{-2}{5}$ x - 2

Step-by-step explanation:

Let us revise some rules

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -1

∵ The equation of the line is 5y = 10 + 2x

- Put the equation in the form of slope-intercept

- Divide both sides by 5

∴ y = 2 + $\frac{2}{5}$ x

∴ m = $\frac{2}{5}$

∴ The slope of the line is $\frac{2}{5}$

∵ The product of the slopes of the perpendicular lines is -1

- That means if the slope of a line is m, then the slope of the

perpendicular line to this line is $\frac{-1}{m}$

∵ The slope of the line = $\frac{2}{5}$

∴ The slope of the perpendicular line $\frac{-5}{2}$

The slope of a line that is perpendicular to a line whose equation

is 5y = 10 + 2x is $\frac{-5}{2}$

∵ Line a is represented by the equation y = -2x + 3

∴ m = -2

∴ The slope of the line is -2

∵ The equation of the line is y = 2x - 1

∴ m = 2

∴ The slope of the line is 2

∵ 2 ≠ -2

∵ 2 × -2 ≠ -1

∴ The two lines neither parallel nor perpendicular

The line y = 2x - 1 is neither parallel nor perpendicular to the line

y = -2x + 3

∵ The equation of the line is y = -2x + 5

∴ m = -2

∴ The slope of the line is -2

∵ The slopes of the lines are equal

∴ The two lines are parallel

The line y = -2x + 5 is parallel to the line y = -2x + 3

∵ The equation of the line is y = $\frac{1}{2}$ x + 7

∴ m = $\frac{1}{2}$

∴ The slope of the line is $\frac{1}{2}$

∵ $\frac{1}{2}$ × -2 = -1

∵ The product of the slopes of the lines is -1

∴ The two lines are perpendicular

The line y = $\frac{1}{2}$ x + 7 is perpendicular to the line

y = -2x + 3

∵ The equation of a line that is parallel to the line whose equation

is 2x + 5y = 10

∴ Their slopes are equal

- Put the equation in the form of y = mx + b to find m

∵ 2x + 5y = 10

- Subtract 2x from both sides

∴ 5y = 10 - 2x

- Divide both sides

∴ y = 2 - $\frac{2}{5}$ x

∴ m = $\frac{-2}{5}$

∴ The slope of the line is $\frac{-2}{5}$

∵ The form of the equation is y = mx + b

∵ m = $\frac{-2}{5}$

∴ y = $\frac{-2}{5}$ x + b

∵ The line passes through the point (5 , -4)

- Substitute the coordinates of the point in the equation to find b

∵ x = 5 , y = -4

∴ -4 = $\frac{-2}{5}$ (5) + b

∴ -4 = -2 + b

- Add 2 to both sides

∴ -2 = b

∴ y = $\frac{-2}{5}$ x - 2

The equation of a line that passes through the point (5 , -4) and

is parallel to the line whose equation is 2x + 5y = 10 is

y = $\frac{-2}{5}$ x - 2

Learn more:

You can learn more about the equation of a line in brainly.com/question/4152194

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