QuestionSolve for $\mathrm{x}$ and $\mathrm{y}$ using substitution or elimination from these equations: $5x + 1 = y + 5$ and $10x + 8 = 1 - 3y$ .

Studdy Solution

STEP 1

Assumptions1. The system of equations is linear. . The system of equations has a solution.

STEP 2

First, we need to isolate one variable in one of the equations. We can start with the first equation by isolating $\mathrm{y}$ .
$y =5x +1 -5$

STEP 3

implify the equation to get $\mathrm{y}$ in terms of $\mathrm{x}$ .
$y =5x -$

STEP 4

Now, we substitute $\mathrm{y}$ from the first equation into the second equation. This gives us a new equation in terms of $\mathrm{x}$ only.
$10x +8 =1 -3(x -4)$

STEP 5

Expand the right side of the equation.
$10x +8 =1 -15x +12$

STEP 6

Combine like terms on the right side of the equation.
$10x +8 = -15x +13$

STEP 7

Rearrange the equation to get all terms involving $\mathrm{x}$ on one side and the constant term on the other side.
$10x +15x =13 -$

STEP 8

Combine like terms on both sides of the equation.
$25x =5$

STEP 9

olve for $\mathrm{x}$ by dividing both sides of the equation by25.
$x =5 /25$

STEP 10

implify the right side of the equation to get the value of $\mathrm{x}$ .
$x =0.2$

STEP 11

Now that we have the value of $\mathrm{x}$ , we can substitute this into the equation for $\mathrm{y}$ that we derived in3.
$y =5(0.) -4$

STEP 12

implify the right side of the equation to get the value of $\mathrm{y}$ .
$y = -4$

STEP 13

implify the right side of the equation to get the value of $\mathrm{y}$ .
$y = -3$ The solution to the system of equations is $\mathrm{x} =0.2$ and $\mathrm{y} = -3$ .

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QuestionSolve for $\mathrm{x}$ and $\mathrm{y}$ using substitution or elimination from these equations: $5x + 1 = y + 5$ and $10x + 8 = 1 - 3y$ .

Studdy Solution

STEP 1

Assumptions1. The system of equations is linear. . The system of equations has a solution.

STEP 2

First, we need to isolate one variable in one of the equations. We can start with the first equation by isolating $\mathrm{y}$ .
$y =5x +1 -5$

STEP 3

implify the equation to get $\mathrm{y}$ in terms of $\mathrm{x}$ .
$y =5x -$

STEP 4

Now, we substitute $\mathrm{y}$ from the first equation into the second equation. This gives us a new equation in terms of $\mathrm{x}$ only.
$10x +8 =1 -3(x -4)$

STEP 5

Expand the right side of the equation.
$10x +8 =1 -15x +12$

STEP 6

Combine like terms on the right side of the equation.
$10x +8 = -15x +13$

STEP 7

Rearrange the equation to get all terms involving $\mathrm{x}$ on one side and the constant term on the other side.
$10x +15x =13 -$

STEP 8

Combine like terms on both sides of the equation.
$25x =5$

STEP 9

olve for $\mathrm{x}$ by dividing both sides of the equation by25.
$x =5 /25$

STEP 10

implify the right side of the equation to get the value of $\mathrm{x}$ .
$x =0.2$

STEP 11

Now that we have the value of $\mathrm{x}$ , we can substitute this into the equation for $\mathrm{y}$ that we derived in3.
$y =5(0.) -4$

STEP 12

implify the right side of the equation to get the value of $\mathrm{y}$ .
$y = -4$

STEP 13

implify the right side of the equation to get the value of $\mathrm{y}$ .
$y = -3$ The solution to the system of equations is $\mathrm{x} =0.2$ and $\mathrm{y} = -3$ .

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QuestionSolve for x\mathrm{x}x and y\mathrm{y}y using substitution or elimination from these equations: 5x+1=y+55x + 1 = y + 55x+1=y+5 and 10x+8=1−3y10x + 8 = 1 - 3y10x+8=1−3y.

Studdy Solution

STEP 1

Assumptions1. The system of equations is linear. . The system of equations has a solution.

STEP 2

First, we need to isolate one variable in one of the equations. We can start with the first equation by isolating y\mathrm{y}y.y=5x+1−5y =5x +1 -5y=5x+1−5

STEP 3

implify the equation to get y\mathrm{y}y in terms of x\mathrm{x}x.y=5x−y =5x -y=5x−

STEP 4

Now, we substitute y\mathrm{y}y from the first equation into the second equation. This gives us a new equation in terms of x\mathrm{x}x only.10x+8=1−3(x−4)10x +8 =1 -3(x -4)10x+8=1−3(x−4)

STEP 5

Expand the right side of the equation.10x+8=1−15x+1210x +8 =1 -15x +1210x+8=1−15x+12

STEP 6

Combine like terms on the right side of the equation.10x+8=−15x+1310x +8 = -15x +1310x+8=−15x+13

STEP 7

Rearrange the equation to get all terms involving x\mathrm{x}x on one side and the constant term on the other side.10x+15x=13−10x +15x =13 -10x+15x=13−

STEP 8

Combine like terms on both sides of the equation.25x=525x =525x=5

STEP 9

olve for x\mathrm{x}x by dividing both sides of the equation by25.x=5/25x =5 /25x=5/25

STEP 10

implify the right side of the equation to get the value of x\mathrm{x}x.x=0.2x =0.2x=0.2

STEP 11

Now that we have the value of x\mathrm{x}x, we can substitute this into the equation for y\mathrm{y}y that we derived in3.y=5(0.)−4y =5(0.) -4y=5(0.)−4

STEP 12

implify the right side of the equation to get the value of y\mathrm{y}y.y=−4y = -4y=−4

STEP 13

implify the right side of the equation to get the value of y\mathrm{y}y.y=−3y = -3y=−3The solution to the system of equations is x=0.2\mathrm{x} =0.2x=0.2 and y=−3\mathrm{y} = -3y=−3.

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QuestionSolve for $\mathrm{x}$ and $\mathrm{y}$ using substitution or elimination from these equations: $5x + 1 = y + 5$ and $10x + 8 = 1 - 3y$ .

First, we need to isolate one variable in one of the equations. We can start with the first equation by isolating $\mathrm{y}$ .
$y =5x +1 -5$

implify the equation to get $\mathrm{y}$ in terms of $\mathrm{x}$ .
$y =5x -$

Now, we substitute $\mathrm{y}$ from the first equation into the second equation. This gives us a new equation in terms of $\mathrm{x}$ only.
$10x +8 =1 -3(x -4)$

Expand the right side of the equation.
$10x +8 =1 -15x +12$

Combine like terms on the right side of the equation.
$10x +8 = -15x +13$

Rearrange the equation to get all terms involving $\mathrm{x}$ on one side and the constant term on the other side.
$10x +15x =13 -$

Combine like terms on both sides of the equation.
$25x =5$

olve for $\mathrm{x}$ by dividing both sides of the equation by25.
$x =5 /25$

implify the right side of the equation to get the value of $\mathrm{x}$ .
$x =0.2$

Now that we have the value of $\mathrm{x}$ , we can substitute this into the equation for $\mathrm{y}$ that we derived in3.
$y =5(0.) -4$

implify the right side of the equation to get the value of $\mathrm{y}$ .
$y = -4$

implify the right side of the equation to get the value of $\mathrm{y}$ .
$y = -3$ The solution to the system of equations is $\mathrm{x} =0.2$ and $\mathrm{y} = -3$ .