Solve a System of Linear Equations: x + y = 12, x

Math Problem Statement

Solve the system of linear equations: x + y = 12, x - y = 2.

The image contains a system of linear equations:

x + y = 12 \\ x - y = 2 \end{cases}$$ To solve this system, we can use either the substitution method or the elimination method. I'll use the elimination method here. 1. **Add the two equations together** to eliminate $$y$$: $$(x + y) + (x - y) = 12 + 2$$ This simplifies to: $$2x = 14$$ So, $$x = \frac{14}{2} = 7$$ 2. **Substitute $$x = 7$$** into the first equation $$x + y = 12$$ to find $$y$$: $$7 + y = 12$$ Subtract 7 from both sides: $$y = 12 - 7 = 5$$ Thus, the solution to the system is: $$x = 7, \quad y = 5$$ Would you like any further details or explanations? Here are some additional related questions: 1. How can the substitution method be used to solve this system? 2. What is the geometric interpretation of the solution? 3. How can you verify the solution is correct? 4. What are some other methods for solving systems of linear equations? 5. What happens if the system of equations is dependent? **Tip:** When using the elimination method, it's helpful to add or subtract the equations directly if they are already set up to cancel out one of the variables.

Drop file here or Click Here to upload

Algebra
Linear Equations
Systems of Equations

x + y = 12
x - y = 2

Elimination Method

Grades 6-8

Solving the System of Equations: x + 2y = 12 and x - 2y = 0

Solve the System of Linear Equations: x + y = 11, 2x + y = 12

Solve the System of Linear Equations: x - 2y = 4, x + y - 12 = 4 - 3y

Solving the System of Linear Equations: 2x + 3y = 12, 4x - y = 5

Solve the System of Equations x + y = 5 and -x + 2y = 4