At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
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].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.