Math Problem Statement
What is the value of x in the solution to the system of equations?
-2x + y = 6
x - y = 1
Solution
We are given the following system of equations to solve for :
-2x + y &= 6 \\ x - y &= 1 \end{aligned}$$ ### Step 1: Solve one equation for one variable. We can solve the second equation for $$y$$: $$x - y = 1 \quad \Rightarrow \quad y = x - 1$$ ### Step 2: Substitute the expression for $$y$$ into the first equation. Substitute $$y = x - 1$$ into the first equation: $$-2x + (x - 1) = 6$$ Simplify the equation: $$-2x + x - 1 = 6 \quad \Rightarrow \quad -x - 1 = 6$$ ### Step 3: Solve for $$x$$. Now, solve for $$x$$: $$-x = 6 + 1 \quad \Rightarrow \quad -x = 7 \quad \Rightarrow \quad x = -7$$ So, the value of $$x$$ is $$-7$$. The correct answer is **B. -7**. Would you like more details or have any questions? Here are five related questions to expand on this: 1. How do you solve a system of equations using the substitution method? 2. How can you check if the solution to a system of equations is correct? 3. What are the different methods to solve a system of linear equations? 4. What happens if both equations in a system are multiples of each other? 5. Can a system of equations have no solution or infinite solutions? How would you recognize it? **Tip**: Always substitute your found values back into the original equations to verify your solution!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Substitution Method
Formulas
x - y = 1, y = x - 1
-2x + (x - 1) = 6
Theorems
Substitution Theorem
Suitable Grade Level
Grades 8-10