QuestionFind the intersection of the lines defined by $y=x+2$ and $y=-2x+17$ .

Studdy Solution

STEP 1

Assumptions1. The equations given are linear equations in two variables, x and y. . The equations are in the form of y = mx + c, where m is the slope and c is the y-intercept.
3. The solution to these equations is the point where the two lines intersect.

STEP 2

To find the solution, we need to set the two equations equal to each other and solve for x.
$x +2 = -2x +17$

STEP 3

Next, we need to bring all the x terms to one side of the equation and the constants to the other side. We can do this by adding2x to both sides and subtracting2 from both sides.
$x +2x =17 -2$

STEP 4

implify the equation to find the value of x.
$3x =15$

STEP 5

To solve for x, we need to divide both sides of the equation by3.
$x =15 /3$

STEP 6

Calculate the value of x.
$x =15 /3 =5$

STEP 7

Now that we have the value of x, we can substitute it into the first equation to find the value of y.
$y =5 +2$

STEP 8

Calculate the value of y.
$y =5 +2 =7$ The solution to the system of equations is (5,7).

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QuestionFind the intersection of the lines defined by $y=x+2$ and $y=-2x+17$ .

Studdy Solution

STEP 1

Assumptions1. The equations given are linear equations in two variables, x and y. . The equations are in the form of y = mx + c, where m is the slope and c is the y-intercept.
3. The solution to these equations is the point where the two lines intersect.

STEP 2

To find the solution, we need to set the two equations equal to each other and solve for x.
$x +2 = -2x +17$

STEP 3

Next, we need to bring all the x terms to one side of the equation and the constants to the other side. We can do this by adding2x to both sides and subtracting2 from both sides.
$x +2x =17 -2$

STEP 4

implify the equation to find the value of x.
$3x =15$

STEP 5

To solve for x, we need to divide both sides of the equation by3.
$x =15 /3$

STEP 6

Calculate the value of x.
$x =15 /3 =5$

STEP 7

Now that we have the value of x, we can substitute it into the first equation to find the value of y.
$y =5 +2$

STEP 8

Calculate the value of y.
$y =5 +2 =7$ The solution to the system of equations is (5,7).

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QuestionFind the intersection of the lines defined by y=x+2y=x+2y=x+2 and y=−2x+17y=-2x+17y=−2x+17.

Studdy Solution

STEP 1

Assumptions1. The equations given are linear equations in two variables, x and y. . The equations are in the form of y = mx + c, where m is the slope and c is the y-intercept.3. The solution to these equations is the point where the two lines intersect.

STEP 2

To find the solution, we need to set the two equations equal to each other and solve for x.x+2=−2x+17x +2 = -2x +17x+2=−2x+17

STEP 3

Next, we need to bring all the x terms to one side of the equation and the constants to the other side. We can do this by adding2x to both sides and subtracting2 from both sides.x+2x=17−2x +2x =17 -2x+2x=17−2

STEP 4

implify the equation to find the value of x.3x=153x =153x=15

STEP 5

To solve for x, we need to divide both sides of the equation by3.x=15/3x =15 /3x=15/3

STEP 6

Calculate the value of x.x=15/3=5x =15 /3 =5x=15/3=5

STEP 7

Now that we have the value of x, we can substitute it into the first equation to find the value of y.y=5+2y =5 +2y=5+2

STEP 8

Calculate the value of y.y=5+2=7y =5 +2 =7y=5+2=7The solution to the system of equations is (5,7).

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Studdy solves anything!

Start learning now

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

QuestionFind the intersection of the lines defined by $y=x+2$ and $y=-2x+17$ .

Assumptions1. The equations given are linear equations in two variables, x and y. . The equations are in the form of y = mx + c, where m is the slope and c is the y-intercept.
3. The solution to these equations is the point where the two lines intersect.

To find the solution, we need to set the two equations equal to each other and solve for x.
$x +2 = -2x +17$

Next, we need to bring all the x terms to one side of the equation and the constants to the other side. We can do this by adding2x to both sides and subtracting2 from both sides.
$x +2x =17 -2$

implify the equation to find the value of x.
$3x =15$

To solve for x, we need to divide both sides of the equation by3.
$x =15 /3$

Calculate the value of x.
$x =15 /3 =5$

Now that we have the value of x, we can substitute it into the first equation to find the value of y.
$y =5 +2$

Calculate the value of y.
$y =5 +2 =7$ The solution to the system of equations is (5,7).