Math / Algebra

QuestionSolve the following system of equations graphically on the set of axes below. $\begin{array}{l} y=-x-8 \\ 2 x-y=2 \end{array}$
Plot two lines by the fieng the staph Click a line for detete it.

Studdy Solution

STEP 1

1. The system of equations consists of two linear equations.
2. We need to solve the system graphically, meaning we will find the point where the two lines intersect.
3. The solution to the system is the point $(x, y)$ that satisfies both equations.

STEP 2

1. Rewrite the second equation in slope-intercept form.
2. Plot the first equation on the graph.
3. Plot the second equation on the graph.
4. Identify the point of intersection.
5. Verify the solution by substituting back into the original equations.

STEP 3

The second equation is $2x - y = 2$ . We need to rewrite it in slope-intercept form $y = mx + b$ .
Subtract $2x$ from both sides:
$-y = -2x + 2$
Multiply through by $-1$ to solve for $y$ :
$y = 2x - 2$

STEP 4

The first equation is $y = -x - 8$ .
To plot this equation, identify the y-intercept and the slope:
- The y-intercept is $-8$ , so the point $(0, -8)$ is on the graph. - The slope is $-1$ , meaning for every 1 unit increase in $x$ , $y$ decreases by 1 unit.
Plot the y-intercept and use the slope to find another point. For example, from $(0, -8)$ , move 1 unit to the right and 1 unit down to $(1, -9)$ .
Draw the line through these points.

STEP 5

The second equation is $y = 2x - 2$ .
To plot this equation, identify the y-intercept and the slope:
- The y-intercept is $-2$ , so the point $(0, -2)$ is on the graph. - The slope is $2$ , meaning for every 1 unit increase in $x$ , $y$ increases by 2 units.
Plot the y-intercept and use the slope to find another point. For example, from $(0, -2)$ , move 1 unit to the right and 2 units up to $(1, 0)$ .
Draw the line through these points.

STEP 6

Identify the point where the two lines intersect. This point is the solution to the system of equations.
By examining the graph, the lines intersect at the point $(-2, -6)$ .

STEP 7

Verify the solution by substituting $(-2, -6)$ back into the original equations:
For the first equation $y = -x - 8$ :
$-6 = -(-2) - 8$ $-6 = 2 - 8$ $-6 = -6$ (True)
For the second equation $2x - y = 2$ :
$2(-2) - (-6) = 2$ $-4 + 6 = 2$ $2 = 2$ (True)
Both equations are satisfied, confirming the solution.
The solution is:
$\boxed{(-2, -6)}$

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QuestionSolve the following system of equations graphically on the set of axes below. $\begin{array}{l} y=-x-8 \\ 2 x-y=2 \end{array}$
Plot two lines by the fieng the staph Click a line for detete it.

Studdy Solution

STEP 1

1. The system of equations consists of two linear equations.
2. We need to solve the system graphically, meaning we will find the point where the two lines intersect.
3. The solution to the system is the point $(x, y)$ that satisfies both equations.

STEP 2

1. Rewrite the second equation in slope-intercept form.
2. Plot the first equation on the graph.
3. Plot the second equation on the graph.
4. Identify the point of intersection.
5. Verify the solution by substituting back into the original equations.

STEP 3

The second equation is $2x - y = 2$ . We need to rewrite it in slope-intercept form $y = mx + b$ .
Subtract $2x$ from both sides:
$-y = -2x + 2$
Multiply through by $-1$ to solve for $y$ :
$y = 2x - 2$

STEP 4

STEP 5

STEP 6

Identify the point where the two lines intersect. This point is the solution to the system of equations.
By examining the graph, the lines intersect at the point $(-2, -6)$ .

STEP 7

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QuestionSolve the following system of equations graphically on the set of axes below. y=−x−82x−y=2\begin{array}{l} y=-x-8 \\ 2 x-y=2 \end{array}y=−x−82x−y=2​Plot two lines by the fieng the staph Click a line for detete it.

Studdy Solution

STEP 1

1. The system of equations consists of two linear equations.2. We need to solve the system graphically, meaning we will find the point where the two lines intersect.3. The solution to the system is the point (x,y)(x, y)(x,y) that satisfies both equations.

STEP 2

1. Rewrite the second equation in slope-intercept form.2. Plot the first equation on the graph.3. Plot the second equation on the graph.4. Identify the point of intersection.5. Verify the solution by substituting back into the original equations.

STEP 3

The second equation is 2x−y=22x - y = 22x−y=2. We need to rewrite it in slope-intercept form y=mx+by = mx + by=mx+b.Subtract 2x2x2x from both sides:−y=−2x+2 -y = -2x + 2 −y=−2x+2Multiply through by −1-1−1 to solve for yyy:y=2x−2 y = 2x - 2 y=2x−2

STEP 4

STEP 5

STEP 6

Identify the point where the two lines intersect. This point is the solution to the system of equations.By examining the graph, the lines intersect at the point (−2,−6)(-2, -6)(−2,−6).

STEP 7

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Studdy solves anything!

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

QuestionSolve the following system of equations graphically on the set of axes below. $\begin{array}{l} y=-x-8 \\ 2 x-y=2 \end{array}$
Plot two lines by the fieng the staph Click a line for detete it.

1. The system of equations consists of two linear equations.
2. We need to solve the system graphically, meaning we will find the point where the two lines intersect.
3. The solution to the system is the point $(x, y)$ that satisfies both equations.

1. Rewrite the second equation in slope-intercept form.
2. Plot the first equation on the graph.
3. Plot the second equation on the graph.
4. Identify the point of intersection.
5. Verify the solution by substituting back into the original equations.

The second equation is $2x - y = 2$ . We need to rewrite it in slope-intercept form $y = mx + b$ .
Subtract $2x$ from both sides:
$-y = -2x + 2$
Multiply through by $-1$ to solve for $y$ :
$y = 2x - 2$

Identify the point where the two lines intersect. This point is the solution to the system of equations.
By examining the graph, the lines intersect at the point $(-2, -6)$ .