At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Sure, let's solve the system of equations step by step to find the correct representation and the solution. The system of equations given is:
1. [tex]\( x - 2y = 5 \)[/tex]
2. [tex]\( 3x + 15y = -6 \)[/tex]
First, let’s solve these equations simultaneously.
### Step 1: Convert them into a standard form
The equations are already in a usable form:
- Equation 1: [tex]\( x - 2y = 5 \)[/tex]
- Equation 2: [tex]\( 3x + 15y = -6 \)[/tex]
### Step 2: Solve Equation 1 for [tex]\( x \)[/tex]
From the first equation:
[tex]\[ x = 2y + 5 \][/tex]
### Step 3: Substitute this expression into Equation 2
Substituting [tex]\( x \)[/tex] from Equation 1 into Equation 2:
[tex]\[ 3(2y + 5) + 15y = -6 \][/tex]
### Step 4: Simplify and solve for [tex]\( y \)[/tex]
Distributing the 3 in the second equation:
[tex]\[ 6y + 15 + 15y = -6 \][/tex]
Combine like terms:
[tex]\[ 21y + 15 = -6 \][/tex]
Subtract 15 from both sides:
[tex]\[ 21y = -21 \][/tex]
Divide by 21:
[tex]\[ y = -1 \][/tex]
### Step 5: Solve for [tex]\( x \)[/tex]
Now substitute [tex]\( y = -1 \)[/tex] back into the expression for [tex]\( x \)[/tex]:
[tex]\[ x = 2(-1) + 5 \][/tex]
[tex]\[ x = -2 + 5 \][/tex]
[tex]\[ x = 3 \][/tex]
So, the solution to the system of equations is:
[tex]\[ (x, y) = (3, -1) \][/tex]
### Conclusion
Therefore, the ordered pair [tex]\( (3, -1) \)[/tex] is the solution to the system, and the graph that correctly represents the given system of equations should intersect at this point [tex]\( (3, -1) \)[/tex].
To complete the sentence:
"The graph that correctly represents the given system of equations is graph [tex]\( \square \)[/tex] and the solution to the system is ( [tex]\(3, -1\)[/tex] )"
You will need to refer to the graphs presented (Graph A, B, C, D) to identify which graph intersects at [tex]\( (3, -1) \)[/tex].
1. [tex]\( x - 2y = 5 \)[/tex]
2. [tex]\( 3x + 15y = -6 \)[/tex]
First, let’s solve these equations simultaneously.
### Step 1: Convert them into a standard form
The equations are already in a usable form:
- Equation 1: [tex]\( x - 2y = 5 \)[/tex]
- Equation 2: [tex]\( 3x + 15y = -6 \)[/tex]
### Step 2: Solve Equation 1 for [tex]\( x \)[/tex]
From the first equation:
[tex]\[ x = 2y + 5 \][/tex]
### Step 3: Substitute this expression into Equation 2
Substituting [tex]\( x \)[/tex] from Equation 1 into Equation 2:
[tex]\[ 3(2y + 5) + 15y = -6 \][/tex]
### Step 4: Simplify and solve for [tex]\( y \)[/tex]
Distributing the 3 in the second equation:
[tex]\[ 6y + 15 + 15y = -6 \][/tex]
Combine like terms:
[tex]\[ 21y + 15 = -6 \][/tex]
Subtract 15 from both sides:
[tex]\[ 21y = -21 \][/tex]
Divide by 21:
[tex]\[ y = -1 \][/tex]
### Step 5: Solve for [tex]\( x \)[/tex]
Now substitute [tex]\( y = -1 \)[/tex] back into the expression for [tex]\( x \)[/tex]:
[tex]\[ x = 2(-1) + 5 \][/tex]
[tex]\[ x = -2 + 5 \][/tex]
[tex]\[ x = 3 \][/tex]
So, the solution to the system of equations is:
[tex]\[ (x, y) = (3, -1) \][/tex]
### Conclusion
Therefore, the ordered pair [tex]\( (3, -1) \)[/tex] is the solution to the system, and the graph that correctly represents the given system of equations should intersect at this point [tex]\( (3, -1) \)[/tex].
To complete the sentence:
"The graph that correctly represents the given system of equations is graph [tex]\( \square \)[/tex] and the solution to the system is ( [tex]\(3, -1\)[/tex] )"
You will need to refer to the graphs presented (Graph A, B, C, D) to identify which graph intersects at [tex]\( (3, -1) \)[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.