QuestionSolve the system of equations: $6x - 4y = -8$ and $y = -6x + 2$ .

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations. . The equations are in the form of $ax + by = c$ and $y = dx + e$ .
3. We are tasked to find the values of $x$ and $y$ that satisfy both equations.

STEP 2

The system of equations is given as $\left\{\begin{array}{c}6 x-4 y=-8 \\ y=-6 x+2\end{array}\right.$

STEP 3

We can use substitution method to solve this system of equations. Since the second equation is already solved for $y$ , we can substitute $y$ in the first equation with $-6x +2$ .
$6x -(-6x +2) = -8$

STEP 4

istribute the $-4$ to both terms inside the parentheses.
$6x +24x -8 = -8$

STEP 5

Combine like terms on the left side of the equation.
$30x -8 = -8$

STEP 6

Add $8$ to both sides of the equation to isolate $30x$ on one side.
$30x =0$

STEP 7

Divide both sides of the equation by $30$ to solve for $x$ .
$x =0$

STEP 8

Now that we have the value of $x$ , we can substitute $x =0$ into the second equation to solve for $y$ .
$y = -6(0) +2$

STEP 9

implify the equation to find the value of $y$ .
$y =2$ The solution to the system of equations is $x =$ and $y =2$ .

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QuestionSolve the system of equations: $6x - 4y = -8$ and $y = -6x + 2$ .

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations. . The equations are in the form of $ax + by = c$ and $y = dx + e$ .
3. We are tasked to find the values of $x$ and $y$ that satisfy both equations.

STEP 2

The system of equations is given as $\left\{\begin{array}{c}6 x-4 y=-8 \\ y=-6 x+2\end{array}\right.$

STEP 3

We can use substitution method to solve this system of equations. Since the second equation is already solved for $y$ , we can substitute $y$ in the first equation with $-6x +2$ .
$6x -(-6x +2) = -8$

STEP 4

istribute the $-4$ to both terms inside the parentheses.
$6x +24x -8 = -8$

STEP 5

Combine like terms on the left side of the equation.
$30x -8 = -8$

STEP 6

Add $8$ to both sides of the equation to isolate $30x$ on one side.
$30x =0$

STEP 7

Divide both sides of the equation by $30$ to solve for $x$ .
$x =0$

STEP 8

Now that we have the value of $x$ , we can substitute $x =0$ into the second equation to solve for $y$ .
$y = -6(0) +2$

STEP 9

implify the equation to find the value of $y$ .
$y =2$ The solution to the system of equations is $x =$ and $y =2$ .

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QuestionSolve the system of equations: 6x−4y=−86x - 4y = -86x−4y=−8 and y=−6x+2y = -6x + 2y=−6x+2.

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations. . The equations are in the form of ax+by=cax + by = cax+by=c and y=dx+ey = dx + ey=dx+e.3. We are tasked to find the values of xxx and yyy that satisfy both equations.

STEP 2

The system of equations is given as{6x−4y=−8y=−6x+2\left\{\begin{array}{c}6 x-4 y=-8 \\ y=-6 x+2\end{array}\right.{6x−4y=−8y=−6x+2​

STEP 3

We can use substitution method to solve this system of equations. Since the second equation is already solved for yyy, we can substitute yyy in the first equation with −6x+2-6x +2−6x+2.6x−(−6x+2)=−86x -(-6x +2) = -86x−(−6x+2)=−8

STEP 4

istribute the −4-4−4 to both terms inside the parentheses.6x+24x−8=−86x +24x -8 = -86x+24x−8=−8

STEP 5

Combine like terms on the left side of the equation.30x−8=−830x -8 = -830x−8=−8

STEP 6

Add 888 to both sides of the equation to isolate 30x30x30x on one side.30x=030x =030x=0

STEP 7

Divide both sides of the equation by 303030 to solve for xxx.x=0x =0x=0

STEP 8

Now that we have the value of xxx, we can substitute x=0x =0x=0 into the second equation to solve for yyy.y=−6(0)+2y = -6(0) +2y=−6(0)+2

STEP 9

implify the equation to find the value of yyy.y=2y =2y=2The solution to the system of equations is x=x =x= and y=2y =2y=2.

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QuestionSolve the system of equations: $6x - 4y = -8$ and $y = -6x + 2$ .

Assumptions1. We have a system of two linear equations. . The equations are in the form of $ax + by = c$ and $y = dx + e$ .
3. We are tasked to find the values of $x$ and $y$ that satisfy both equations.

The system of equations is given as $\left\{\begin{array}{c}6 x-4 y=-8 \\ y=-6 x+2\end{array}\right.$

We can use substitution method to solve this system of equations. Since the second equation is already solved for $y$ , we can substitute $y$ in the first equation with $-6x +2$ .
$6x -(-6x +2) = -8$

istribute the $-4$ to both terms inside the parentheses.
$6x +24x -8 = -8$

Combine like terms on the left side of the equation.
$30x -8 = -8$

Add $8$ to both sides of the equation to isolate $30x$ on one side.
$30x =0$

Divide both sides of the equation by $30$ to solve for $x$ .
$x =0$

Now that we have the value of $x$ , we can substitute $x =0$ into the second equation to solve for $y$ .
$y = -6(0) +2$

implify the equation to find the value of $y$ .
$y =2$ The solution to the system of equations is $x =$ and $y =2$ .