Math / Algebra

QuestionVALUATE
Independent Practice \begin{tabular}{l|ll|} \hline \begin{tabular}{l} I can write, solve, interpret, and justify my solution \\ method for systems of linear equations using \\ multiple methods (graphing, substitution, and \\ linear combination). \end{tabular} & Starting... & Getting There... Got it! \\ \hline \end{tabular} Complete the previous problems, check your solutions, then complete the Lesson Checkpoint below. Complete the Lesson Reflection above by circling your current understanding of the Learning Goal(s). Use the system of equations $\left\{\begin{array}{l}x+y=20 \\ x-4 y=-20\end{array}\right.$
1. Solve by adding or subtracting.
The solution is $\qquad$
2. Which graph justifies your solution is correct? Select one.
lifelong Algebra 1A (2024) Module 4

Studdy Solution

STEP 1

What is this asking? We've got two equations with $x$ and $y$ , and we need to find the values of $x$ and $y$ that make both equations true.
Then, we need to pick the graph that shows the solution. Watch out! Make sure you check your answer in both equations!
It's easy to make a small mistake, so checking is key.

STEP 2

1. Solve the system of equations.
2. Identify the correct graph.

STEP 3

We're given these two equations: $x + y = 20$ $x - 4y = -20$

STEP 4

Notice that both equations have just one $x$ .
If we subtract the second equation from the first equation, the $x$ terms will add to zero!
This is called the elimination method.
Let's do it! $(x + y) - (x - 4y) = 20 - (-20)$

STEP 5

Distribute the subtraction in the left side and simplify both sides: $x + y - x + 4y = 20 + 20$ $5y = 40$

STEP 6

Divide both sides by $\textbf{5}$ to isolate $y$ : $\frac{5y}{5} = \frac{40}{5}$ $y = \textbf{8}$ Great! We found that $y = \textbf{8}$ .

STEP 7

Let's use the first equation, $x + y = 20$ , because it looks simpler.
Substitute $y = \textbf{8}$ : $x + \textbf{8} = 20$

STEP 8

Subtract $\textbf{8}$ from both sides: $x + 8 - 8 = 20 - 8$ $x = \textbf{12}$ Awesome! We found $x = \textbf{12}$ .

STEP 9

Our solution is $x = \textbf{12}$ and $y = \textbf{8}$ .
This means the lines representing the two equations intersect at the point $(12, 8)$ .

STEP 10

The correct graph will be the one where the two lines cross at the point where $x = 12$ and $y = 8$ .

STEP 11

The solution to the system of equations is $x = \textbf{12}$ and $y = \textbf{8}$ .
The graph that shows this solution is the one where the lines intersect at the point $\textbf{(12, 8)}$ .

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Studdy Solution

STEP 1

STEP 2

1. Solve the system of equations.
2. Identify the correct graph.

STEP 3

We're given these two equations: $x + y = 20$ $x - 4y = -20$

STEP 4

Notice that both equations have just one $x$ .
If we subtract the second equation from the first equation, the $x$ terms will add to zero!
This is called the elimination method.
Let's do it! $(x + y) - (x - 4y) = 20 - (-20)$

STEP 5

Distribute the subtraction in the left side and simplify both sides: $x + y - x + 4y = 20 + 20$ $5y = 40$

STEP 6

Divide both sides by $\textbf{5}$ to isolate $y$ : $\frac{5y}{5} = \frac{40}{5}$ $y = \textbf{8}$ Great! We found that $y = \textbf{8}$ .

STEP 7

Let's use the first equation, $x + y = 20$ , because it looks simpler.
Substitute $y = \textbf{8}$ : $x + \textbf{8} = 20$

STEP 8

Subtract $\textbf{8}$ from both sides: $x + 8 - 8 = 20 - 8$ $x = \textbf{12}$ Awesome! We found $x = \textbf{12}$ .

STEP 9

Our solution is $x = \textbf{12}$ and $y = \textbf{8}$ .
This means the lines representing the two equations intersect at the point $(12, 8)$ .

STEP 10

The correct graph will be the one where the two lines cross at the point where $x = 12$ and $y = 8$ .

STEP 11

The solution to the system of equations is $x = \textbf{12}$ and $y = \textbf{8}$ .
The graph that shows this solution is the one where the lines intersect at the point $\textbf{(12, 8)}$ .

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Studdy Solution

STEP 1

STEP 2

1. Solve the system of equations.2. Identify the correct graph.

STEP 3

We're given these two equations: x+y=20 x + y = 20 x+y=20 x−4y=−20 x - 4y = -20 x−4y=−20

STEP 4

Notice that both equations have just one xxx.If we subtract the second equation from the first equation, the xxx terms will add to zero!This is called the **elimination method**.Let's do it! (x+y)−(x−4y)=20−(−20) (x + y) - (x - 4y) = 20 - (-20) (x+y)−(x−4y)=20−(−20)

STEP 5

Distribute the subtraction in the left side and simplify both sides: x+y−x+4y=20+20 x + y - x + 4y = 20 + 20 x+y−x+4y=20+20 5y=40 5y = 40 5y=40

STEP 6

Divide both sides by 5\textbf{5}5 to isolate yyy: 5y5=405 \frac{5y}{5} = \frac{40}{5} 55y​=540​ y=8 y = \textbf{8} y=8Great! We found that y=8y = \textbf{8}y=8.

STEP 7

Let's use the first equation, x+y=20x + y = 20x+y=20, because it looks simpler.Substitute y=8y = \textbf{8}y=8: x+8=20 x + \textbf{8} = 20 x+8=20

STEP 8

Subtract 8\textbf{8}8 from both sides: x+8−8=20−8 x + 8 - 8 = 20 - 8 x+8−8=20−8 x=12 x = \textbf{12} x=12Awesome! We found x=12x = \textbf{12}x=12.

STEP 9

Our solution is x=12x = \textbf{12}x=12 and y=8y = \textbf{8}y=8.This means the lines representing the two equations intersect at the point (12,8)(12, 8)(12,8).

STEP 10

The correct graph will be the one where the two lines cross at the point where x=12x = 12x=12 and y=8y = 8y=8.

STEP 11

The solution to the system of equations is x=12x = \textbf{12}x=12 and y=8y = \textbf{8}y=8.The graph that shows this solution is the one where the lines intersect at the point (12, 8)\textbf{(12, 8)}(12, 8).

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Start learning now

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

1. Solve the system of equations.
2. Identify the correct graph.

We're given these two equations: $x + y = 20$ $x - 4y = -20$

Notice that both equations have just one $x$ .
If we subtract the second equation from the first equation, the $x$ terms will add to zero!
This is called the elimination method.
Let's do it! $(x + y) - (x - 4y) = 20 - (-20)$

Distribute the subtraction in the left side and simplify both sides: $x + y - x + 4y = 20 + 20$ $5y = 40$

Divide both sides by $\textbf{5}$ to isolate $y$ : $\frac{5y}{5} = \frac{40}{5}$ $y = \textbf{8}$ Great! We found that $y = \textbf{8}$ .

Let's use the first equation, $x + y = 20$ , because it looks simpler.
Substitute $y = \textbf{8}$ : $x + \textbf{8} = 20$

Subtract $\textbf{8}$ from both sides: $x + 8 - 8 = 20 - 8$ $x = \textbf{12}$ Awesome! We found $x = \textbf{12}$ .

Our solution is $x = \textbf{12}$ and $y = \textbf{8}$ .
This means the lines representing the two equations intersect at the point $(12, 8)$ .

The correct graph will be the one where the two lines cross at the point where $x = 12$ and $y = 8$ .

The solution to the system of equations is $x = \textbf{12}$ and $y = \textbf{8}$ .
The graph that shows this solution is the one where the lines intersect at the point $\textbf{(12, 8)}$ .