Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Sure, let's solve this system of linear equations step by step.
We are given the system of equations:
[tex]\[ \begin{cases} -7x - 2y = 14 \\ 6x + 6y = 18 \end{cases} \][/tex]
### Step 1: Simplify the Equations if Possible
First, we’ll simplify the second equation:
[tex]\[ 6x + 6y = 18 \][/tex]
Divide every term by 6:
[tex]\[ x + y = 3 \quad \text{(Equation 2)} \][/tex]
### Step 2: Use Substitution or Elimination
We can use the substitution method here. Express [tex]\(y\)[/tex] from Equation 2:
[tex]\[ y = 3 - x \quad \text{(Equation 3)} \][/tex]
### Step 3: Substitute into the First Equation
Now, substitute Equation 3 into the first equation:
[tex]\[ -7x - 2(3 - x) = 14 \][/tex]
Simplify this equation:
[tex]\[ -7x - 6 + 2x = 14 \][/tex]
Combine like terms:
[tex]\[ -5x - 6 = 14 \][/tex]
Add 6 to both sides:
[tex]\[ -5x = 20 \][/tex]
Divide both sides by -5:
[tex]\[ x = -4 \][/tex]
### Step 4: Substitute [tex]\(x\)[/tex] Back into Equation 3
Now, substitute [tex]\(x = -4\)[/tex] back into Equation 3:
[tex]\[ y = 3 - (-4) \][/tex]
Simplify:
[tex]\[ y = 3 + 4 \\ y = 7 \][/tex]
### Step 5: Write the Solution
Therefore, the solution to the system of equations is:
[tex]\[ x = -4 \][/tex]
[tex]\[ y = 7 \][/tex]
We can now fill in the blanks:
[tex]\[ x = -4 \][/tex]
[tex]\[ y = 7 \][/tex]
This means the solution to the system of equations is [tex]\((-4, 7)\)[/tex].
We are given the system of equations:
[tex]\[ \begin{cases} -7x - 2y = 14 \\ 6x + 6y = 18 \end{cases} \][/tex]
### Step 1: Simplify the Equations if Possible
First, we’ll simplify the second equation:
[tex]\[ 6x + 6y = 18 \][/tex]
Divide every term by 6:
[tex]\[ x + y = 3 \quad \text{(Equation 2)} \][/tex]
### Step 2: Use Substitution or Elimination
We can use the substitution method here. Express [tex]\(y\)[/tex] from Equation 2:
[tex]\[ y = 3 - x \quad \text{(Equation 3)} \][/tex]
### Step 3: Substitute into the First Equation
Now, substitute Equation 3 into the first equation:
[tex]\[ -7x - 2(3 - x) = 14 \][/tex]
Simplify this equation:
[tex]\[ -7x - 6 + 2x = 14 \][/tex]
Combine like terms:
[tex]\[ -5x - 6 = 14 \][/tex]
Add 6 to both sides:
[tex]\[ -5x = 20 \][/tex]
Divide both sides by -5:
[tex]\[ x = -4 \][/tex]
### Step 4: Substitute [tex]\(x\)[/tex] Back into Equation 3
Now, substitute [tex]\(x = -4\)[/tex] back into Equation 3:
[tex]\[ y = 3 - (-4) \][/tex]
Simplify:
[tex]\[ y = 3 + 4 \\ y = 7 \][/tex]
### Step 5: Write the Solution
Therefore, the solution to the system of equations is:
[tex]\[ x = -4 \][/tex]
[tex]\[ y = 7 \][/tex]
We can now fill in the blanks:
[tex]\[ x = -4 \][/tex]
[tex]\[ y = 7 \][/tex]
This means the solution to the system of equations is [tex]\((-4, 7)\)[/tex].
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.