Math Problem Statement
Solve using substitution.
y = x + 6 y = –x − 4
( , )
Solution
To solve this system of equations using substitution, we'll substitute the expression for from the first equation into the second equation.
Step 1: Write the equations
Step 2: Substitute the expression for from the first equation into the second equation
We know that , so substitute this into the second equation:
Step 3: Solve for
Now solve for : Add to both sides: Subtract 6 from both sides: Divide by 2:
Step 4: Substitute back into one of the original equations to find
Use the first equation :
Final Answer
The solution to the system of equations is .
Do you need further explanation or have any questions?
Related questions:
- How do you solve a system of linear equations using the elimination method?
- What are the different methods for solving a system of equations?
- How can you check if a solution is correct in a system of equations?
- What does it mean if a system of equations has no solution or infinitely many solutions?
- Can you solve a system of equations with more than two variables using substitution?
Tip:
When using substitution, always choose the equation where one variable is already isolated, as it simplifies the substitution process.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Equations
Substitution Method
Formulas
y = x + 6
y = -x - 4
Theorems
Substitution method for solving systems of equations
Suitable Grade Level
Grades 7-9
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