Math Problem Statement
Find two pairs of coordinates for each equation by making a T-chart. Use the coordinates to graph the lines and find the solution. x + 2y = 6 2x - 3y = 12
Solution
To solve the system of equations by graphing, we'll first create T-charts for each equation, find pairs of coordinates, and then use these to graph the lines.
Step 1: Solve for y in each equation.
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First equation:
Solve for :
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Second equation:
Solve for :
Step 2: Create T-Charts and Find Coordinates
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For :
Choose values for and find corresponding values.
Coordinates 0 3 (0, 3) 2 2 (2, 2) 4 1 (4, 1) -
For :
Choose values for and find corresponding values.
Coordinates 0 -4 (0, -4) 3 -2 (3, -2) 6 0 (6, 0)
Step 3: Graph the Lines and Find the Solution
- Plot the coordinates from both T-charts on a graph.
- Draw lines through the points for each equation.
- The intersection point of these two lines will be the solution to the system.
If you graph these correctly, you will find that the lines intersect at the point , which is the solution to the system of equations.
Solution:
The solution is .
Do you have any questions, or would you like further details on any part of this process?
Related Questions:
- What happens if two lines do not intersect?
- How can we verify the solution using substitution?
- Can the solution be a fraction or decimal?
- What if the lines overlap completely?
- What method can be used if graphing is not practical?
Tip: Always double-check your graphs by substituting the intersection point back into both original equations!
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Math Problem Analysis
Mathematical Concepts
Linear equations
Graphing lines
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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