Solve the System of Linear Equations: y = -2x + 7 and y = 5x

Math Problem Statement

Solve the system of equations y = -2x + 7 and y = 5x - 7. Determine the values of x and y.

Let's analyze the system of equations and the graph provided to solve for $x$ and $y$ .

The system of equations given is:

y = -2x + 7 \\ y = 5x - 7 \end{cases}$$ To find the solution to this system of equations, we can set the two equations equal to each other since they both equal $$y$$: $$-2x + 7 = 5x - 7$$ Now, solve for $$x$$: 1. Combine like terms: $$7 + 7 = 5x + 2x$$ $$14 = 7x$$ 2. Divide both sides by 7: $$x = 2$$ Now substitute $$x = 2$$ back into one of the original equations to find $$y$$. Using the first equation: $$y = -2(2) + 7$$ $$y = -4 + 7$$ $$y = 3$$ Thus, the solution to the system of equations is: $$x = 2$$ $$y = 3$$ These values are the coordinates of the intersection point of the two lines. According to the graph, the intersection point at $$(2, 3)$$ confirms our solution. Would you like more details or have any questions about the solution? Here are some related questions to consider: 1. How do you solve a system of equations using the substitution method? 2. What is the graphical interpretation of solving a system of equations? 3. How can you verify the solution of a system of equations algebraically? 4. What are the different methods to solve a system of linear equations? 5. How can you interpret the solution to a system of equations in a real-world context? **Tip:** When solving systems of equations graphically, always check the intersection point to ensure it satisfies both equations.

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Algebra
Linear Equations
Graphing

y = mx + b

The Intersection of Two Lines

Grades 8-10

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