Solved on Feb 15, 2024

Solve the system of linear equations $y=5$ and $-3x+4y=8$ .

STEP 1

Assumptions
1. We have a system of linear equations: $\left\{\begin{array}{r} y=5 \\ -3x+4y=8 \end{array}\right.$
2. We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

STEP 2

Since the first equation directly gives us the value of $y$ , we can use it to find $x$ by substituting $y$ into the second equation.
$y=5$

STEP 3

Substitute $y=5$ into the second equation:
$-3x + 4(5) = 8$

STEP 4

Simplify the equation by multiplying 4 by 5:
$-3x + 20 = 8$

STEP 5

Subtract 20 from both sides of the equation to isolate the term with $x$ :
$-3x = 8 - 20$

STEP 6

Calculate the right-hand side of the equation:
$-3x = -12$

STEP 7

Divide both sides of the equation by $-3$ to solve for $x$ :
$x = \frac{-12}{-3}$

STEP 8

Calculate the value of $x$ :
$x = 4$

STEP 9

Now that we have the value of $x$ , we can state the solution to the system of equations. We already know that $y=5$ from the first equation.
The solution to the system of equations is $x=4$ and $y=5$ .

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Solve the system of linear equations $y=5$ and $-3x+4y=8$ .

STEP 1

Assumptions
1. We have a system of linear equations: $\left\{\begin{array}{r} y=5 \\ -3x+4y=8 \end{array}\right.$
2. We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

STEP 2

Since the first equation directly gives us the value of $y$ , we can use it to find $x$ by substituting $y$ into the second equation.
$y=5$

STEP 3

Substitute $y=5$ into the second equation:
$-3x + 4(5) = 8$

STEP 4

Simplify the equation by multiplying 4 by 5:
$-3x + 20 = 8$

STEP 5

Subtract 20 from both sides of the equation to isolate the term with $x$ :
$-3x = 8 - 20$

STEP 6

Calculate the right-hand side of the equation:
$-3x = -12$

STEP 7

Divide both sides of the equation by $-3$ to solve for $x$ :
$x = \frac{-12}{-3}$

STEP 8

Calculate the value of $x$ :
$x = 4$

STEP 9

Now that we have the value of $x$ , we can state the solution to the system of equations. We already know that $y=5$ from the first equation.
The solution to the system of equations is $x=4$ and $y=5$ .

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Solve the system of linear equations y=5y=5y=5 and −3x+4y=8-3x+4y=8−3x+4y=8.

STEP 1

Assumptions1. We have a system of linear equations: {y=5−3x+4y=8\left\{\begin{array}{r} y=5 \\ -3x+4y=8 \end{array}\right.{y=5−3x+4y=8​2. We need to find the values of xxx and yyy that satisfy both equations simultaneously.

STEP 2

Since the first equation directly gives us the value of yyy, we can use it to find xxx by substituting yyy into the second equation.y=5y=5y=5

STEP 3

Substitute y=5y=5y=5 into the second equation:−3x+4(5)=8-3x + 4(5) = 8−3x+4(5)=8

STEP 4

Simplify the equation by multiplying 4 by 5:−3x+20=8-3x + 20 = 8−3x+20=8

STEP 5

Subtract 20 from both sides of the equation to isolate the term with xxx:−3x=8−20-3x = 8 - 20−3x=8−20

STEP 6

Calculate the right-hand side of the equation:−3x=−12-3x = -12−3x=−12

STEP 7

Divide both sides of the equation by −3-3−3 to solve for xxx:x=−12−3x = \frac{-12}{-3}x=−3−12​

STEP 8

Calculate the value of xxx:x=4x = 4x=4

STEP 9

Now that we have the value of xxx, we can state the solution to the system of equations. We already know that y=5y=5y=5 from the first equation.The solution to the system of equations is x=4x=4x=4 and y=5y=5y=5.

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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 $y=5$ and $-3x+4y=8$ .

Assumptions
1. We have a system of linear equations: $\left\{\begin{array}{r} y=5 \\ -3x+4y=8 \end{array}\right.$
2. We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

Since the first equation directly gives us the value of $y$ , we can use it to find $x$ by substituting $y$ into the second equation.
$y=5$

Substitute $y=5$ into the second equation:
$-3x + 4(5) = 8$

Simplify the equation by multiplying 4 by 5:
$-3x + 20 = 8$

Subtract 20 from both sides of the equation to isolate the term with $x$ :
$-3x = 8 - 20$

Calculate the right-hand side of the equation:
$-3x = -12$

Divide both sides of the equation by $-3$ to solve for $x$ :
$x = \frac{-12}{-3}$

Calculate the value of $x$ :
$x = 4$

Now that we have the value of $x$ , we can state the solution to the system of equations. We already know that $y=5$ from the first equation.
The solution to the system of equations is $x=4$ and $y=5$ .