Math Problem Statement
The given system of equations had a solution(x,y) what is the value of x?
The given system of equations has a solution (x, y). What is the value of x?
Solution
Let's solve the system of equations provided in the image:
The system is:
3x + y &= 3 \\ 7x - y &= 2 \end{aligned}$$ We can solve this by elimination or substitution. I'll use the elimination method: 1. Add the two equations together to eliminate $$y$$: $$(3x + y) + (7x - y) = 3 + 2$$ Simplifying: $$10x = 5$$ So, $$x = \frac{5}{10} = 0.5$$ Thus, the value of $$x$$ is $$0.5$$. Would you like to solve for $$y$$ as well, or need more clarification? ### Follow-up questions: 1. What is the value of $$y$$ using this solution? 2. How would the solution change if the second equation had a different constant? 3. Can you solve the same system using substitution instead of elimination? 4. What does it mean geometrically to solve a system of linear equations? 5. How do we determine if a system of linear equations has no solution or infinitely many solutions? **Tip**: Always double-check your work by substituting the solution back into the original equations!Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Systems of Equations
Formulas
Addition or elimination method for solving systems
Substitution method for solving systems
Theorems
Linear equation properties
System of equations with two variables
Suitable Grade Level
Grades 8-10