QuestionSolve the system of equations: $7x + 3y = 0$ and $-5x + 10y = 0$ .

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations. . The equations are $7x +3y =0$ and $-5x +10y =0$ .
3. We are looking for the values of $x$ and $y$ that satisfy both equations.

STEP 2

We start by simplifying the second equation. We can do this by dividing the entire equation by $-5$ .
$\frac{-5x +10y}{-5} = \frac{0}{-5}$

STEP 3

After simplifying, we get $x -2y =0$ This is our new second equation.

STEP 4

Now we have two equations that are easier to work with1. $7x +3y =0$
2. $x -2y =0$

STEP 5

Next, we can solve the second equation for $x$ .
$x =2y$

STEP 6

Now we substitute $x =2y$ into the first equation.
$(2y) +3y =0$

STEP 7

implify the equation by multiplying $7$ by $2y$ .
$14y +3y =0$

STEP 8

Combine like terms.
$17y =0$

STEP 9

To find the value of $y$ , divide both sides of the equation by $17$ .
$y = \frac{}{17}$

STEP 10

implify to get the value of $y$ .
$y =0$

STEP 11

Now that we have $y =0$ , we can substitute this into the equation $x =y$ .
$x =(0)$

STEP 12

implify to get the value of $x$ .
$x =0$ So, the solution to the system of equations is $x =0$ and $y =0$ .

Was this helpful?

QuestionSolve the system of equations: $7x + 3y = 0$ and $-5x + 10y = 0$ .

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations. . The equations are $7x +3y =0$ and $-5x +10y =0$ .
3. We are looking for the values of $x$ and $y$ that satisfy both equations.

STEP 2

We start by simplifying the second equation. We can do this by dividing the entire equation by $-5$ .
$\frac{-5x +10y}{-5} = \frac{0}{-5}$

STEP 3

After simplifying, we get $x -2y =0$ This is our new second equation.

STEP 4

Now we have two equations that are easier to work with1. $7x +3y =0$
2. $x -2y =0$

STEP 5

Next, we can solve the second equation for $x$ .
$x =2y$

STEP 6

Now we substitute $x =2y$ into the first equation.
$(2y) +3y =0$

STEP 7

implify the equation by multiplying $7$ by $2y$ .
$14y +3y =0$

STEP 8

Combine like terms.
$17y =0$

STEP 9

To find the value of $y$ , divide both sides of the equation by $17$ .
$y = \frac{}{17}$

STEP 10

implify to get the value of $y$ .
$y =0$

STEP 11

Now that we have $y =0$ , we can substitute this into the equation $x =y$ .
$x =(0)$

STEP 12

implify to get the value of $x$ .
$x =0$ So, the solution to the system of equations is $x =0$ and $y =0$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the system of equations: 7x+3y=07x + 3y = 07x+3y=0 and −5x+10y=0-5x + 10y = 0−5x+10y=0.

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations. . The equations are 7x+3y=07x +3y =07x+3y=0 and −5x+10y=0-5x +10y =0−5x+10y=0.3. We are looking for the values of xxx and yyy that satisfy both equations.

STEP 2

We start by simplifying the second equation. We can do this by dividing the entire equation by −5-5−5.−5x+10y−5=0−5\frac{-5x +10y}{-5} = \frac{0}{-5}−5−5x+10y​=−50​

STEP 3

After simplifying, we getx−2y=0x -2y =0x−2y=0This is our new second equation.

STEP 4

Now we have two equations that are easier to work with1. 7x+3y=07x +3y =07x+3y=02. x−2y=0x -2y =0x−2y=0

STEP 5

Next, we can solve the second equation for xxx.x=2yx =2yx=2y

STEP 6

Now we substitute x=2yx =2yx=2y into the first equation.(2y)+3y=0(2y) +3y =0(2y)+3y=0

STEP 7

implify the equation by multiplying 777 by 2y2y2y.14y+3y=014y +3y =014y+3y=0

STEP 8

Combine like terms.17y=017y =017y=0

STEP 9

To find the value of yyy, divide both sides of the equation by 171717.y=17y = \frac{}{17}y=17​

STEP 10

implify to get the value of yyy.y=0y =0y=0

STEP 11

Now that we have y=0y =0y=0, we can substitute this into the equation x=yx =yx=y.x=(0)x =(0)x=(0)

STEP 12

implify to get the value of xxx.x=0x =0x=0So, the solution to the system of equations is x=0x =0x=0 and y=0y =0y=0.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the system of equations: $7x + 3y = 0$ and $-5x + 10y = 0$ .

Assumptions1. We have a system of two linear equations. . The equations are $7x +3y =0$ and $-5x +10y =0$ .
3. We are looking for the values of $x$ and $y$ that satisfy both equations.

We start by simplifying the second equation. We can do this by dividing the entire equation by $-5$ .
$\frac{-5x +10y}{-5} = \frac{0}{-5}$

After simplifying, we get $x -2y =0$ This is our new second equation.

Now we have two equations that are easier to work with1. $7x +3y =0$
2. $x -2y =0$

Next, we can solve the second equation for $x$ .
$x =2y$

Now we substitute $x =2y$ into the first equation.
$(2y) +3y =0$

implify the equation by multiplying $7$ by $2y$ .
$14y +3y =0$

Combine like terms.
$17y =0$

To find the value of $y$ , divide both sides of the equation by $17$ .
$y = \frac{}{17}$

implify to get the value of $y$ .
$y =0$

Now that we have $y =0$ , we can substitute this into the equation $x =y$ .
$x =(0)$

implify to get the value of $x$ .
$x =0$ So, the solution to the system of equations is $x =0$ and $y =0$ .