Can someone please help answer?

Solve the system of equations. y = -5x + 24 y = 4x - 21 a. ( -5, -1) c. ( -1, 5) b. ( 5, -1) d. No solution

Svetlanka [38]

y = -5x + 24

y = 4x - 21

Since both of these equations are equal to Y, theyre equal to each other.

So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.

-5x + 24 = 4x - 21

Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:

-5x + 24 - 24 = 4x - 21 - 24

-5x = 4x - 45

Now we subtract 4x from both sides so the 4x shift to the other side

-5x - 4x = 4x - 4x - 45

-9x = -45

Finally divide both sides by -9 so x is by itself

(-9)÷(-9x) = -(45)÷(-9)

x = 5

Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.

Now apply x = 5 to either of the initial equations to find the value of Y

y = -5x + 24 or y = 4x - 21

(I'll do both but u only need one)

y = -5(5) + 24

y = -25 + 24

y = -1

y = 4(5) - 21

y = 20 - 21

y = -1

Either way, X is 5 and Y is -1

Answer (5, -1)

5 0

3 years ago

Perpendicular to the line 4x - 6y + 7 = 0 , passing through (3, 4) .

PilotLPTM [1.2K]

Answer:

The equation of line perpendicular to given line passing through (3,4) is:

$y = -\frac{3}{2}x+\frac{17}{2}$

Step-by-step explanation:

Given equation of line is:

$4x - 6y + 7 = 0$

Given equation is in standard form. It has to be converted into slope-intercept form to extract slope from the equation.

So,

$4x+7 = 6y\\6y=4x+7\\\frac{6y}{6} = \frac{4x+7}{6}\\y = \frac{4}{6}x+\frac{7}{6}\\y=\frac{2}{3}x+\frac{7}{6}$

The standard form of slope-intercept form of equation is:

$y=mx+b$

Here, the co-efficient of x is the slope of the line.

So the slope of given line is: 2/3

m = 2/3

The product of slopes of two perpendicular lines is -1

Let m1 be the slope of line perpendicular to given line

Then

$m.m_1 = -1\\\frac{2}{3} . m_1 = -1\\m_1 = -1*\frac{3}{2}\\m_1 = -\frac{3}{2}$

The equation of perpendicular will be:

$y = m_1x+b$

Putting the value of slope

$y = -\frac{3}{2}x+b$

To find the value of b, putting (3,4) in the equation

$4 = -\frac{3}{2}(3)+b\\4 = -\frac{9}{2}+b\\b = 4+\frac{9}{2}\\b= \frac{8+9}{2}\\b=\frac{17}{2}$

So the equation of line perpendicular to given line passing through (3,4) is:

$y = -\frac{3}{2}x+\frac{17}{2}$

7 0

3 years ago

Are 5y=2x-5 and 5y-3x=1 parallel

alexandr1967 [171]

Convert to ax+by=c form
for
ax+by=c
and
dx+ey=f
a/d=b/e
then they are paralell

5y=2x-5
-2x+5y=-5

5y-3x=1
-3x+5y=1

compare
-2x+5y=-5
-3x+5y=1

-2/-3=5/5
2/3=1
false
they are not paralelll

5 0

3 years ago

I screenshotted my question.

andrey2020 [161]

Answer:

Step-by-step explanation:

Hello,

$4-4x\leq 24\\\\\text{We can divide by 4.}\\\\1-x\leq 6\\\\\text{We can add x.}\\\\1\leq x+6\\\\\text{We can subtract 6.}\\\\1-6=-5\leq x \large \boxed{\sf \bf x \in [-5;+\infty[}$