Solved on Mar 03, 2024

Solve the system of linear equations $x-y=4$ and $x+2y=4$ for $x$ and $y$ .

STEP 1

Assumptions
1. We have a system of linear equations: $\left\{\begin{array}{l} x - y = 4 \\ x + 2y = 4 \end{array}\right.$
2. We will use substitution method to solve the system.

STEP 2

First, we solve one of the equations for one variable. Let's solve the first equation for $x$ .
$x = y + 4$

STEP 3

Now, we substitute $x$ in the second equation with the expression we found in STEP_2.
$(y + 4) + 2y = 4$

STEP 4

Combine like terms in the equation.
$3y + 4 = 4$

STEP 5

Subtract 4 from both sides to isolate the term with $y$ .
$3y = 0$

STEP 6

Divide both sides by 3 to solve for $y$ .
$y = \frac{0}{3}$

STEP 7

Calculate the value of $y$ .
$y = 0$

STEP 8

Now that we have the value of $y$ , we substitute it back into the expression we found for $x$ in STEP_2.
$x = 0 + 4$

STEP 9

Calculate the value of $x$ .
$x = 4$
The solution to the system of equations is $x = 4$ and $y = 0$ .

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Solve the system of linear equations $x-y=4$ and $x+2y=4$ for $x$ and $y$ .

STEP 1

Assumptions
1. We have a system of linear equations: $\left\{\begin{array}{l} x - y = 4 \\ x + 2y = 4 \end{array}\right.$
2. We will use substitution method to solve the system.

STEP 2

First, we solve one of the equations for one variable. Let's solve the first equation for $x$ .
$x = y + 4$

STEP 3

Now, we substitute $x$ in the second equation with the expression we found in STEP_2.
$(y + 4) + 2y = 4$

STEP 4

Combine like terms in the equation.
$3y + 4 = 4$

STEP 5

Subtract 4 from both sides to isolate the term with $y$ .
$3y = 0$

STEP 6

Divide both sides by 3 to solve for $y$ .
$y = \frac{0}{3}$

STEP 7

Calculate the value of $y$ .
$y = 0$

STEP 8

Now that we have the value of $y$ , we substitute it back into the expression we found for $x$ in STEP_2.
$x = 0 + 4$

STEP 9

Calculate the value of $x$ .
$x = 4$
The solution to the system of equations is $x = 4$ and $y = 0$ .

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Solve the system of linear equations x−y=4x-y=4x−y=4 and x+2y=4x+2y=4x+2y=4 for xxx and yyy.

STEP 1

Assumptions1. We have a system of linear equations: {x−y=4x+2y=4 \left\{\begin{array}{l} x - y = 4 \\ x + 2y = 4 \end{array}\right. {x−y=4x+2y=4​2. We will use substitution method to solve the system.

STEP 2

First, we solve one of the equations for one variable. Let's solve the first equation for x x x.x=y+4 x = y + 4 x=y+4

STEP 3

Now, we substitute x x x in the second equation with the expression we found in STEP_2.(y+4)+2y=4 (y + 4) + 2y = 4 (y+4)+2y=4

STEP 4

Combine like terms in the equation.3y+4=4 3y + 4 = 4 3y+4=4

STEP 5

Subtract 4 from both sides to isolate the term with y y y.3y=0 3y = 0 3y=0

STEP 6

Divide both sides by 3 to solve for y y y.y=03 y = \frac{0}{3} y=30​

STEP 7

Calculate the value of y y y.y=0 y = 0 y=0

STEP 8

Now that we have the value of y y y, we substitute it back into the expression we found for x x x in STEP_2.x=0+4 x = 0 + 4 x=0+4

STEP 9

Calculate the value of x x x.x=4 x = 4 x=4The solution to the system of equations is x=4 x = 4 x=4 and y=0 y = 0 y=0.

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Solve the system of linear equations $x-y=4$ and $x+2y=4$ for $x$ and $y$ .

Assumptions
1. We have a system of linear equations: $\left\{\begin{array}{l} x - y = 4 \\ x + 2y = 4 \end{array}\right.$
2. We will use substitution method to solve the system.

First, we solve one of the equations for one variable. Let's solve the first equation for $x$ .
$x = y + 4$

Now, we substitute $x$ in the second equation with the expression we found in STEP_2.
$(y + 4) + 2y = 4$

Combine like terms in the equation.
$3y + 4 = 4$

Subtract 4 from both sides to isolate the term with $y$ .
$3y = 0$

Divide both sides by 3 to solve for $y$ .
$y = \frac{0}{3}$

Calculate the value of $y$ .
$y = 0$

Now that we have the value of $y$ , we substitute it back into the expression we found for $x$ in STEP_2.
$x = 0 + 4$

Calculate the value of $x$ .
$x = 4$
The solution to the system of equations is $x = 4$ and $y = 0$ .