Math / Algebra

QuestionSolve the system of equations by graphing: $\left\{\begin{aligned} y-2 x & =11 \\ -1 y & =-2 x-11\end{aligned}\right.$ Enter the solution set in the boxes below. If the lines are parallel, enter DNE (for "does not exist") into each box. If the lines are coincident (infinite number of solutions), enter oo into each box. (Note: Use double letter o's, not zeros, for infinity.) $(x, y)=1$ $\square$ $\square$

Studdy Solution

STEP 1

What is this asking? Find the point where two lines intersect by graphing them. Watch out! Don't forget to check if the lines are parallel or the same line!

STEP 2

1. Rewrite equations in slope-intercept form
2. Graph both lines
3. Find the intersection point

STEP 3

Let's start with the first equation: $y - 2x = 11$ .
We want to get $y$ by itself, so add $2x$ to both sides.
This gives us:
\[ y = 2x + 11 $
This is the slope-intercept form $y = mx + b$ , where the slope $m$ is $2$ and the y-intercept $b$ is $11$ .

STEP 4

Now, let's tackle the second equation: $-y = -2x - 11$ .
First, multiply everything by $-1$ to make $y$ positive:
\[ y = 2x + 11 $
Whoa! Look at that!
It's the same equation as the first one!

STEP 5

Since both equations are the same, when we graph them, they'll lie right on top of each other.
This means every point on the line is a solution to the system of equations.

STEP 6

Because the lines are coincident, they intersect at every point along the line.
So, the solution is an infinite number of solutions.

STEP 7

The lines are coincident, so the solution set is $(\text{oo}, \text{oo})$ .

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Studdy Solution

STEP 1

What is this asking? Find the point where two lines intersect by graphing them. Watch out! Don't forget to check if the lines are parallel or the same line!

STEP 2

1. Rewrite equations in slope-intercept form
2. Graph both lines
3. Find the intersection point

STEP 3

Let's start with the first equation: $y - 2x = 11$ .
We want to get $y$ by itself, so add $2x$ to both sides.
This gives us:
\[ y = 2x + 11 $
This is the slope-intercept form $y = mx + b$ , where the slope $m$ is $2$ and the y-intercept $b$ is $11$ .

STEP 4

Now, let's tackle the second equation: $-y = -2x - 11$ .
First, multiply everything by $-1$ to make $y$ positive:
\[ y = 2x + 11 $
Whoa! Look at that!
It's the same equation as the first one!

STEP 5

Since both equations are the same, when we graph them, they'll lie right on top of each other.
This means every point on the line is a solution to the system of equations.

STEP 6

Because the lines are coincident, they intersect at every point along the line.
So, the solution is an infinite number of solutions.

STEP 7

The lines are coincident, so the solution set is $(\text{oo}, \text{oo})$ .

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Studdy Solution

STEP 1

What is this asking? Find the point where two lines intersect by graphing them. Watch out! Don't forget to check if the lines are parallel or the same line!

STEP 2

1. Rewrite equations in slope-intercept form2. Graph both lines3. Find the intersection point

STEP 3

STEP 4

Now, let's tackle the second equation: −y=−2x−11 -y = -2x - 11 −y=−2x−11.First, **multiply** everything by −1-1−1 to make y y y positive:\[ y = 2x + 11 $Whoa! Look at that!It's the same equation as the first one!

STEP 5

Since both equations are the same, when we graph them, they'll lie right on top of each other.This means every point on the line is a solution to the system of equations.

STEP 6

Because the lines are coincident, they intersect at every point along the line.So, the solution is an **infinite number of solutions**.

STEP 7

The lines are coincident, so the solution set is (oo,oo)(\text{oo}, \text{oo})(oo,oo).

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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.

1. Rewrite equations in slope-intercept form
2. Graph both lines
3. Find the intersection point

Now, let's tackle the second equation: $-y = -2x - 11$ .
First, multiply everything by $-1$ to make $y$ positive:
\[ y = 2x + 11 $
Whoa! Look at that!
It's the same equation as the first one!

Since both equations are the same, when we graph them, they'll lie right on top of each other.
This means every point on the line is a solution to the system of equations.

Because the lines are coincident, they intersect at every point along the line.
So, the solution is an infinite number of solutions.

The lines are coincident, so the solution set is $(\text{oo}, \text{oo})$ .