1) 12sin5x+cos5x=9

The solution of two linear equations is (-2,2). One equations has a slope of 3. The slope of the other equation is the negative

Crank

The system of equations is:

$3x-y=-8$

$x+3y=4$

Step-by-step explanation:

Let the line 1 be: $l_1$

Let line 2 be: $l_2$

Both lines will pass through the same point (-2,2)

And

Given

$m_1=3\\m_2=-\frac{1}{3}$

<u>The slope intercept form for first line will be:</u>

$y=m_1x+b$

Putting values

$y=3x+b$

Putting the point in the equation

$2=(-2)(3)+b\\2=-6+b\\b=2+6\\b=8$

So, the equation is: y=3x+8

Converting the equation in standard form

$y=3x+8$

Subtracting y from both sides

$0=3x-y+8$

Subtracting 8 from both sides

$3x-y=-8$

<u>The second line's equation will be:</u>

$y=m_2x+b$

Putting slope

$y=-\frac{1}{3}x+b$

Putting the point

$2=-\frac{1}{3}(-2)+b\\2=\frac{2}{3}+b\\b=2-\frac{2}{3}\\b=\frac{6-2}{3}\\b=\frac{4}{3}$

The equation is:

$y=-\frac{1}{3}x+\frac{4}{3}$

Converting the equation in standard form

Multiplying whole equation by 3

$3y=-x+4$

Adding x on both sides

$x+3y=4$

Hence

The system of equations is:

$3x-y=-8$

$x+3y=4$

Keywords: Equation of line, Linear equation

Learn more about linear equation at:

#LearnwithBrainly

3 0

3 years ago

Help this question for me?!

iogann1982 [59]

Answer:

2.8 pounds

Step-by-step explanation:

6 0

3 years ago

You need to mix 1 2/3 quarts of soda and 4 1/2 quarts of juice to make a fruit punch. which choice is the smallest-sized bowl th

Dmitrij [34]

You want a bowl that can hold 6 1/6 quarts of liquid

5 0

4 years ago

Lucy had math and reading homework tonight. Lucy can solve each math problem in 5 minutes and she can read each page in 2.5 minu

drek231 [11]

Answer:

$x=18,y=6$ , graph is there for reference.

Step-by-step explanation:

Given,

$x$ is the number of math problem Lucy solved.

$y$ is the number of pages she read.

She can do each math problem in $5$ minutes, therefore she can solve $x$ number of questions into $5 \times x=5x$ minutes.

She can read each page in $2.5$ minutes, therefore she can read $y$ pages in 2.5y minutes.

As per given detail,

$5x+2.5y=105$ equation 1.

And,

It is given that number of math problems Lucy solved is 3 times the number of pages she read.

$x=3y$ equation 2.

We need to find $x$ and $y$ intercept of each of the equation to graph them.

For $x-intercept$ put y=0

We will get $x=\frac{105}{5} =21$

Thus the point is $(21,0)$

Let us find $y-intercept$ by assuming $x=0$

we get $y=\frac{105}{2.5} =42$

Thus the point is $(42,0)$

Join these two points.

Similarly considering the other equation $x=3y$

Here x-intercept would be at $y=0$

We will get $x=0$

Thus the point is $(0,0)$

Let us assume on more point, say $x=30$ , we get $y=10$

Thus the point is $(30,10)$

Join these two points.

We will get a point of intersection at $(18,6)$

Thus $x=18$ and $y=6$

8 0

4 years ago

Can someone pleast help me with this

ki77a [65]

You should do sport because it gives you a lot of exercise and makes your body healthy. Sports are important because it makes people happy and it shows from studies that oscillatory increases a lot from sports. Sports are fun and exciting and it boots blood flow to the brain. It controls your body weight and it even makes u gain more skills! Kids have a way of breaking bones but sports help bones strengthen. And sports help with anxiety and even depression! I think kids playing sports are a great ideas because every kid needs some fun once and a while

8 0

3 years ago