Solved on Feb 25, 2024

Solve the system of linear equations $-5x + 8y = 0$ and $-7x - 8y = -96$ .

STEP 1

Assumptions
1. We have a system of two linear equations: \begin{align} -5x + 8y &= 0 \\ -7x - 8y &= -96 \end{align}
2. We need to find the values of $x$ and $y$ that satisfy both equations.

STEP 2

We can use the method of elimination to solve this system of equations. First, we will add the two equations together to eliminate $y$ .

STEP 3

Add the two equations: \begin{align} (-5x + 8y) + (-7x - 8y) &= 0 + (-96) \end{align}

STEP 4

Combine like terms: \begin{align} -5x - 7x + 8y - 8y &= -96 \end{align}

STEP 5

Simplify the equation: \begin{align} -12x &= -96 \end{align}

STEP 6

Divide both sides of the equation by $-12$ to solve for $x$ : \begin{align} x &= \frac{-96}{-12} \end{align}

STEP 7

Calculate the value of $x$ : \begin{align} x &= 8 \end{align}

STEP 8

Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . We will use the first equation: \begin{align} -5x + 8y &= 0 \end{align}

STEP 9

Substitute $x = 8$ into the equation: \begin{align} -5(8) + 8y &= 0 \end{align}

STEP 10

Simplify the equation: \begin{align} -40 + 8y &= 0 \end{align}

STEP 11

Add $40$ to both sides of the equation to solve for $y$ : \begin{align} 8y &= 40 \end{align}

STEP 12

Divide both sides of the equation by $8$ : \begin{align} y &= \frac{40}{8} \end{align}

STEP 13

Calculate the value of $y$ : \begin{align} y &= 5 \end{align}
The solution to the system of equations is $x = 8$ and $y = 5$ .

Was this helpful?

Solve the system of linear equations $-5x + 8y = 0$ and $-7x - 8y = -96$ .

STEP 1

Assumptions
1. We have a system of two linear equations: \begin{align} -5x + 8y &= 0 \\ -7x - 8y &= -96 \end{align}
2. We need to find the values of $x$ and $y$ that satisfy both equations.

STEP 2

We can use the method of elimination to solve this system of equations. First, we will add the two equations together to eliminate $y$ .

STEP 3

Add the two equations: \begin{align} (-5x + 8y) + (-7x - 8y) &= 0 + (-96) \end{align}

STEP 4

Combine like terms: \begin{align} -5x - 7x + 8y - 8y &= -96 \end{align}

STEP 5

Simplify the equation: \begin{align} -12x &= -96 \end{align}

STEP 6

Divide both sides of the equation by $-12$ to solve for $x$ : \begin{align} x &= \frac{-96}{-12} \end{align}

STEP 7

Calculate the value of $x$ : \begin{align} x &= 8 \end{align}

STEP 8

Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . We will use the first equation: \begin{align} -5x + 8y &= 0 \end{align}

STEP 9

Substitute $x = 8$ into the equation: \begin{align} -5(8) + 8y &= 0 \end{align}

STEP 10

Simplify the equation: \begin{align} -40 + 8y &= 0 \end{align}

STEP 11

Add $40$ to both sides of the equation to solve for $y$ : \begin{align} 8y &= 40 \end{align}

STEP 12

Divide both sides of the equation by $8$ : \begin{align} y &= \frac{40}{8} \end{align}

STEP 13

Calculate the value of $y$ : \begin{align} y &= 5 \end{align}
The solution to the system of equations is $x = 8$ and $y = 5$ .

Start learning now

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

Solve the system of linear equations −5x+8y=0-5x + 8y = 0−5x+8y=0 and −7x−8y=−96-7x - 8y = -96−7x−8y=−96.

STEP 1

Assumptions1. We have a system of two linear equations: \begin{align*} -5x + 8y &= 0 \\ -7x - 8y &= -96 \end{align*}2. We need to find the values of xxx and yyy that satisfy both equations.

STEP 2

We can use the method of elimination to solve this system of equations. First, we will add the two equations together to eliminate yyy.

STEP 3

Add the two equations: \begin{align*} (-5x + 8y) + (-7x - 8y) &= 0 + (-96) \end{align*}

STEP 4

Combine like terms: \begin{align*} -5x - 7x + 8y - 8y &= -96 \end{align*}

STEP 5

Simplify the equation: \begin{align*} -12x &= -96 \end{align*}

STEP 6

Divide both sides of the equation by −12-12−12 to solve for xxx: \begin{align*} x &= \frac{-96}{-12} \end{align*}

STEP 7

Calculate the value of xxx: \begin{align*} x &= 8 \end{align*}

STEP 8

Now that we have the value of xxx, we can substitute it back into one of the original equations to solve for yyy. We will use the first equation: \begin{align*} -5x + 8y &= 0 \end{align*}

STEP 9

Substitute x=8x = 8x=8 into the equation: \begin{align*} -5(8) + 8y &= 0 \end{align*}

STEP 10

Simplify the equation: \begin{align*} -40 + 8y &= 0 \end{align*}

STEP 11

Add 404040 to both sides of the equation to solve for yyy: \begin{align*} 8y &= 40 \end{align*}

STEP 12

Divide both sides of the equation by 888: \begin{align*} y &= \frac{40}{8} \end{align*}

STEP 13

Calculate the value of yyy: \begin{align*} y &= 5 \end{align*}The solution to the system of equations is x=8x = 8x=8 and y=5y = 5y=5.

Start learning now

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

Solve the system of linear equations $-5x + 8y = 0$ and $-7x - 8y = -96$ .

Assumptions
1. We have a system of two linear equations: \begin{align} -5x + 8y &= 0 \\ -7x - 8y &= -96 \end{align}
2. We need to find the values of $x$ and $y$ that satisfy both equations.

We can use the method of elimination to solve this system of equations. First, we will add the two equations together to eliminate $y$ .

Add the two equations: \begin{align} (-5x + 8y) + (-7x - 8y) &= 0 + (-96) \end{align}

Combine like terms: \begin{align} -5x - 7x + 8y - 8y &= -96 \end{align}

Simplify the equation: \begin{align} -12x &= -96 \end{align}

Divide both sides of the equation by $-12$ to solve for $x$ : \begin{align} x &= \frac{-96}{-12} \end{align}

Calculate the value of $x$ : \begin{align} x &= 8 \end{align}

Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . We will use the first equation: \begin{align} -5x + 8y &= 0 \end{align}

Substitute $x = 8$ into the equation: \begin{align} -5(8) + 8y &= 0 \end{align}

Simplify the equation: \begin{align} -40 + 8y &= 0 \end{align}

Add $40$ to both sides of the equation to solve for $y$ : \begin{align} 8y &= 40 \end{align}

Divide both sides of the equation by $8$ : \begin{align} y &= \frac{40}{8} \end{align}

Calculate the value of $y$ : \begin{align} y &= 5 \end{align}
The solution to the system of equations is $x = 8$ and $y = 5$ .