Math Problem Statement

Solve the system of equations by graphing: -x + y = 6, y = 2.

Solution

The problem provided is a system of linear equations that needs to be solved by graphing:

-x + y = 6 \\ y = 2 \end{cases}$$ To solve by graphing: 1. **Rewrite each equation in slope-intercept form (if needed):** - The second equation, $$y = 2$$, is already in slope-intercept form and represents a horizontal line where $$y$$ is always 2. - For the first equation, $$-x + y = 6$$: $$y = x + 6$$ This is a line with a slope of 1 and a y-intercept at 6. 2. **Graph the equations:** - The line $$y = 2$$ is a horizontal line passing through all points where $$y$$ is 2. - The line $$y = x + 6$$ has a slope of 1, meaning it rises one unit up for every unit it moves to the right, and crosses the y-axis at $$(0, 6)$$. 3. **Find the point of intersection:** - Since $$y = 2$$ in both equations at the point of intersection, substitute $$y = 2$$ into the first equation: $$2 = x + 6$$ Solving for $$x$$: $$x = -4$$ - So, the intersection point, which is the solution to the system, is $$(-4, 2)$$. ### Solution: The solution to the system is $$x = -4$$ and $$y = 2$$, or the point $$(-4, 2)$$. Would you like more details on the graphing process or any further explanation? --- ### Related Questions: 1. How would you solve a system of equations with different slopes by graphing? 2. What is the significance of the slope and y-intercept in graphing linear equations? 3. How can you verify the solution of a system of equations using substitution? 4. What if the system of equations had no solutions? How would that appear on a graph? 5. How does graphing help in visualizing systems of linear inequalities? ### Tip: When graphing, always check where lines intersect or if they are parallel.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing Systems of Equations

Formulas

Slope-intercept form y = mx + b

Theorems

None

Suitable Grade Level

Grade 8

Related Recommendation

Solve System of Linear Equations: x + y = 2 and x - 2y = 8

Solving a System of Linear Equations by Graphing: y = 3x - 2 and y = -x + 6

Graphing and Solving a System of Linear Equations: 2x - y = 1 and x + y = 6

Solving Systems of Linear Equations by Graphing: 4x + 2y = -6 and -5x + y = 4

Graphical Solution of System of Equations: y = x + 3 and y = -2x - 6