Write a system of two linear equations in x and y that has the ordered pair solution 

​(55​,33​). 
  
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Part 1

Choose the correct system below.

A.left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals 7 2nd Row 1st Column x minus 2 y equals 13 EndMatrix

left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals 7 2nd Row 1st Column x minus 2 y equals 13 EndMatrix

−2x+y=7

x−2y=13

B.left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals negative 7 2nd Row 1st Column x minus 2 y equals negative 1 EndMatrix

left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals negative 7 2nd Row 1st Column x minus 2 y equals negative 1 EndMatrix

−2x+y=−7

x−2y=−1

C.left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals negative 7 2nd Row 1st Column x minus 2 y equals 1 EndMatrix

left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals negative 7 2nd Row 1st Column x minus 2 y equals 1 EndMatrix

−2x+y=−7

x−2y=1

D.left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals 6 2nd Row 1st Column 2 x plus y equals negative 9 EndMatrix

left brace Start 2 By 1 Matrix 1st Row 1st Column negative 2 x plus y equals 6 2nd Row 1st Column 2 x plus y equals negative 9 EndMatrix

We are asked to find the system of two linear equations that has the ordered pair \( (55, 33) \) as the solution. 

To determine this, we will substitute \( x = 55 \) and \( y = 33 \) into each of the given systems of equations and check which system satisfies both equations.

### Option A:
\[
-2x + y = 7
\]
Substitute \( x = 55 \) and \( y = 33 \):
\[
-2(55) + 33 = -110 + 33 = -77 \neq 7
\]
So, option A is not correct.

### Option B:
\[
-2x + y = -7
\]
Substitute \( x = 55 \) and \( y = 33 \):
\[
-2(55) + 33 = -110 + 33 = -77 \neq -7
\]
So, option B is not correct.

### Option C:
\[
-2x + y = -7
\]
Substitute \( x = 55 \) and \( y = 33 \):
\[
-2(55) + 33 = -110 + 33 = -77 \neq -7
\]
So, option C is not correct.

### Option D:
\[
-2x + y = 6
\]
Substitute \( x = 55 \) and \( y = 33 \):
\[
-2(55) + 33 = -110 + 33 = -77 \neq 6
\]
Now checking the second equation:
\[
2x + y = -9
\]
Substitute \( x = 55 \) and \( y = 33 \):
\[
2(55) + 33 = 110 + 33 = 143 \neq -9
\]
So, option D is also not correct.

---

None of the systems in the options satisfy the ordered pair \( (55, 33) \).

### To Create a Correct System:
Let’s create a system of equations using the ordered pair \( (55, 33) \) as the solution. For example:

1. **Equation 1**: Let’s choose \( 2x - y = 77 \):
   - Substituting \( x = 55 \) and \( y = 33 \):  
   \( 2(55) - 33 = 110 - 33 = 77 \).

2. **Equation 2**: Let’s choose \( x + y = 88 \):
   - Substituting \( x = 55 \) and \( y = 33 \):  
   \( 55 + 33 = 88 \).

So, the system we created is:
\[
\left\{
\begin{array}{l}
2x - y = 77 \\
x + y = 88
\end{array}
\right.
\]
This system has the solution \( (55, 33) \).

Would you like further assistance with another question?

---

### 5 Related Questions:
1. How can we form a system of equations with a given solution?
2. How do you verify that an ordered pair is the solution to a system of equations?
3. What is the method to solve a system of linear equations by substitution?
4. What is the method to solve a system of linear equations by elimination?
5. How do you interpret a solution to a system of linear equations in a real-world context?

### Tip:
To create a system with a specific solution, use the values of \( x \) and \( y \) in each equation, and ensure both equations satisfy the given values.

Write a system of two linear equations in x and y that has the ordered pair solution (55, 33). Choose the correct system from the given options.

Explore how to write and verify a system of two linear equations in x and y with the solution (55, 33). This problem demonstrates key algebraic techniques such as substitution and verification. Ideal for students in Grades 9-10.

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