Math Problem Statement
Graph each equation. Determine the solution of the system of equations. x plus 2 yequals4 3 x plus 2 yequals0 Question content area bottom left Part 1 Use the graphing tool to graph the system.
Part 2 What is the solution of the system of equations? enter your response here (Type an ordered pair.)
Solution
To solve this problem, we will address both parts:
Part 1: Graphing the System of Equations
We are given the system:
To graph these, we first rewrite each equation in slope-intercept form ():
-
For : This equation has:
- Slope () =
- Y-intercept =
-
For : This equation has:
- Slope () =
- Y-intercept = (passes through the origin)
Using these equations, plot both lines on the same graph.
Part 2: Solve for the Intersection Point
The solution to the system is the point where the two lines intersect. To find this algebraically, solve the system:
-
Start with the equations:
-
Subtract equation (1) from equation (2):
-
Substitute into equation (1):
Thus, the solution is:
Graphing Tool
If you are using a graphing tool, plot:
- The line
- The line
Verify that they intersect at .
Do you want details or have any questions?
Here are 5 related questions to expand understanding:
- How do you graph lines given in standard form without rewriting to slope-intercept form?
- How can you solve a system of equations using substitution instead of elimination?
- What are the conditions for a system of linear equations to have no solution?
- How do slopes of two lines determine the type of solution for a system (parallel, intersecting, or coincident)?
- What are some real-world applications of solving systems of linear equations?
Tip: Always double-check calculations when solving systems algebraically to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Graphing Linear Equations
Formulas
Slope-intercept form: y = mx + b
Standard form to slope-intercept form conversion: Ax + By = C → y = -(A/B)x + C/B
Theorems
Intersection of lines in a 2D plane
Suitable Grade Level
Grades 8-10
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