Solved on Feb 19, 2024

Solve the system by graphing: $x-y=5$ and $y=-2$ .

STEP 1

Assumptions
1. We have a system of two linear equations.
2. The first equation is $x - y = 5$ .
3. The second equation is $y = -2$ .
4. We will solve the system by graphing the two equations on the same set of axes.
5. The solution to the system is the point where the two lines intersect.

STEP 2

First, we need to rewrite the first equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$x - y = 5$

STEP 3

Isolate $y$ in the first equation to get it into slope-intercept form.
$-y = -x + 5$

STEP 4

Multiply both sides by -1 to solve for $y$ .
$y = x - 5$

STEP 5

Now we have the first equation in slope-intercept form:
$y = x - 5$

STEP 6

The second equation is already given as $y = -2$ , which is a horizontal line.

STEP 7

To graph the first equation $y = x - 5$ , we can start by plotting the y-intercept, which is $(0, -5)$ .

STEP 8

From the y-intercept, we use the slope, which is 1 (since the coefficient of $x$ is 1), to plot another point. Moving up 1 unit and to the right 1 unit from $(0, -5)$ , we get the point $(1, -4)$ .

STEP 9

Draw the line through the points $(0, -5)$ and $(1, -4)$ , extending it in both directions.

STEP 10

To graph the second equation $y = -2$ , we draw a horizontal line through the y-coordinate of -2 on the y-axis.

STEP 11

The intersection of the two lines is the solution to the system. Since the second line is horizontal at $y = -2$ , it will intersect the first line at the point where the first line has a y-coordinate of -2.

STEP 12

Substitute $y = -2$ into the first equation to find the x-coordinate of the intersection point.
$-2 = x - 5$

STEP 13

Add 5 to both sides of the equation to solve for $x$ .
$x = -2 + 5$

STEP 14

Calculate the value of $x$ .
$x = 3$

STEP 15

The intersection point is $(3, -2)$ , which is the solution to the system.
The solution to the system by graphing is the point $(3, -2)$ .

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Solve the system by graphing: $x-y=5$ and $y=-2$ .

STEP 1

Assumptions
1. We have a system of two linear equations.
2. The first equation is $x - y = 5$ .
3. The second equation is $y = -2$ .
4. We will solve the system by graphing the two equations on the same set of axes.
5. The solution to the system is the point where the two lines intersect.

STEP 2

First, we need to rewrite the first equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$x - y = 5$

STEP 3

Isolate $y$ in the first equation to get it into slope-intercept form.
$-y = -x + 5$

STEP 4

Multiply both sides by -1 to solve for $y$ .
$y = x - 5$

STEP 5

Now we have the first equation in slope-intercept form:
$y = x - 5$

STEP 6

The second equation is already given as $y = -2$ , which is a horizontal line.

STEP 7

To graph the first equation $y = x - 5$ , we can start by plotting the y-intercept, which is $(0, -5)$ .

STEP 8

From the y-intercept, we use the slope, which is 1 (since the coefficient of $x$ is 1), to plot another point. Moving up 1 unit and to the right 1 unit from $(0, -5)$ , we get the point $(1, -4)$ .

STEP 9

Draw the line through the points $(0, -5)$ and $(1, -4)$ , extending it in both directions.

STEP 10

To graph the second equation $y = -2$ , we draw a horizontal line through the y-coordinate of -2 on the y-axis.

STEP 11

The intersection of the two lines is the solution to the system. Since the second line is horizontal at $y = -2$ , it will intersect the first line at the point where the first line has a y-coordinate of -2.

STEP 12

Substitute $y = -2$ into the first equation to find the x-coordinate of the intersection point.
$-2 = x - 5$

STEP 13

Add 5 to both sides of the equation to solve for $x$ .
$x = -2 + 5$

STEP 14

Calculate the value of $x$ .
$x = 3$

STEP 15

The intersection point is $(3, -2)$ , which is the solution to the system.
The solution to the system by graphing is the point $(3, -2)$ .

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Solve the system by graphing: x−y=5x-y=5x−y=5 and y=−2y=-2y=−2.

STEP 1

STEP 2

First, we need to rewrite the first equation in slope-intercept form, which is y=mx+b y = mx + b y=mx+b, where m m m is the slope and b b b is the y-intercept.x−y=5 x - y = 5 x−y=5

STEP 3

Isolate y y y in the first equation to get it into slope-intercept form.−y=−x+5 -y = -x + 5 −y=−x+5

STEP 4

Multiply both sides by -1 to solve for y y y.y=x−5 y = x - 5 y=x−5

STEP 5

Now we have the first equation in slope-intercept form:y=x−5 y = x - 5 y=x−5

STEP 6

The second equation is already given as y=−2 y = -2 y=−2, which is a horizontal line.

STEP 7

To graph the first equation y=x−5 y = x - 5 y=x−5, we can start by plotting the y-intercept, which is (0,−5) (0, -5) (0,−5).

STEP 8

From the y-intercept, we use the slope, which is 1 (since the coefficient of x x x is 1), to plot another point. Moving up 1 unit and to the right 1 unit from (0,−5) (0, -5) (0,−5), we get the point (1,−4) (1, -4) (1,−4).

STEP 9

Draw the line through the points (0,−5) (0, -5) (0,−5) and (1,−4) (1, -4) (1,−4), extending it in both directions.

STEP 10

To graph the second equation y=−2 y = -2 y=−2, we draw a horizontal line through the y-coordinate of -2 on the y-axis.

STEP 11

The intersection of the two lines is the solution to the system. Since the second line is horizontal at y=−2 y = -2 y=−2, it will intersect the first line at the point where the first line has a y-coordinate of -2.

STEP 12

Substitute y=−2 y = -2 y=−2 into the first equation to find the x-coordinate of the intersection point.−2=x−5 -2 = x - 5 −2=x−5

STEP 13

Add 5 to both sides of the equation to solve for x x x.x=−2+5 x = -2 + 5 x=−2+5

STEP 14

Calculate the value of x x x.x=3 x = 3 x=3

STEP 15

The intersection point is (3,−2) (3, -2) (3,−2), which is the solution to the system.The solution to the system by graphing is the point (3,−2) (3, -2) (3,−2).

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Solve the system by graphing: $x-y=5$ and $y=-2$ .

First, we need to rewrite the first equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$x - y = 5$

Isolate $y$ in the first equation to get it into slope-intercept form.
$-y = -x + 5$

Multiply both sides by -1 to solve for $y$ .
$y = x - 5$

Now we have the first equation in slope-intercept form:
$y = x - 5$

The second equation is already given as $y = -2$ , which is a horizontal line.

To graph the first equation $y = x - 5$ , we can start by plotting the y-intercept, which is $(0, -5)$ .

From the y-intercept, we use the slope, which is 1 (since the coefficient of $x$ is 1), to plot another point. Moving up 1 unit and to the right 1 unit from $(0, -5)$ , we get the point $(1, -4)$ .

Draw the line through the points $(0, -5)$ and $(1, -4)$ , extending it in both directions.

To graph the second equation $y = -2$ , we draw a horizontal line through the y-coordinate of -2 on the y-axis.

The intersection of the two lines is the solution to the system. Since the second line is horizontal at $y = -2$ , it will intersect the first line at the point where the first line has a y-coordinate of -2.

Substitute $y = -2$ into the first equation to find the x-coordinate of the intersection point.
$-2 = x - 5$

Add 5 to both sides of the equation to solve for $x$ .
$x = -2 + 5$

Calculate the value of $x$ .
$x = 3$

The intersection point is $(3, -2)$ , which is the solution to the system.
The solution to the system by graphing is the point $(3, -2)$ .