Math Problem Statement

Solve the system of equations by graphing: 4x + 2y = -6 and -5x + y = 4.

Solution

The problem is asking you to solve the following system of linear equations by graphing:

4x + 2y &= -6 \\ -5x + y &= 4 \end{aligned}$$ To find the solution by graphing, let's solve each equation for $$y$$ and then graph them. ### Step 1: Solve each equation for $$y$$ 1. **First equation:** $$4x + 2y = -6$$ Subtract $$4x$$ from both sides: $$2y = -4x - 6$$ Now, divide by 2: $$y = -2x - 3$$ 2. **Second equation:** $$-5x + y = 4$$ Add $$5x$$ to both sides: $$y = 5x + 4$$ ### Step 2: Graph both equations 1. The first equation $$y = -2x - 3$$ is a straight line with a slope of $$-2$$ and a y-intercept of $$-3$$. 2. The second equation $$y = 5x + 4$$ is a straight line with a slope of $$5$$ and a y-intercept of $$4$$. When you graph these two lines, they will intersect at one point, which is the solution to the system of equations. ### Step 3: Solve by substitution or graphing To find the solution algebraically, set the two equations for $$y$$ equal to each other: $$-2x - 3 = 5x + 4$$ Solve for $$x$$: $$-2x - 5x = 4 + 3 \implies -7x = 7 \implies x = -1$$ Now substitute $$x = -1$$ into one of the original equations (e.g., $$y = 5x + 4$$): $$y = 5(-1) + 4 = -5 + 4 = -1$$ Thus, the solution is the ordered pair $$(-1, -1)$$. ### Conclusion The solution to the system of equations is $$(-1, -1)$$. You should select option **A** and input $$(-1, -1)$$ as the ordered pair. --- Would you like more details or have any other questions? ### Related Questions: 1. How do you graph a line using its slope and y-intercept? 2. What is the method for solving a system of equations by substitution? 3. Can a system of linear equations have infinitely many solutions? 4. How can you verify the solution to a system of equations? 5. What are other methods for solving systems of equations (besides graphing)? #### Tip: When solving systems of equations graphically, it's helpful to use precise points (like intercepts) to make the graph accurate.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations
Graphing

Formulas

y = mx + b (Slope-intercept form)
Setting two equations equal to each other for substitution

Theorems

Intersection of two lines to find the solution to a system of linear equations

Suitable Grade Level

Grades 8-10

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