Graphical Simultaneous Equations
This worksheet focuses on solving simultaneous equations graphically, including identifying points of intersection and interpreting solutions on a coordinate plane.
Includes
Standards
Topics
Graphical Simultaneous Equations
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Date:
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Read each question carefully and follow the instructions. Show all your work for full credit. For graphing problems, ensure your lines are clear and labeled.
1. When two linear equations are graphed on the same coordinate plane, what does their point of intersection represent?
The sum of the x-intercepts
A solution that satisfies only one equation
The solution that satisfies both equations simultaneously
The y-intercept of the first equation
2. If two linear equations have the same slope but different y-intercepts, how will their graphs appear?
Intersecting at one point
Coinciding lines
Parallel lines
Perpendicular lines
3. The solution to a system of two linear equations is the point where their graphs .
4. If two equations represent the same line, they have many solutions.
5. Graph the following system of equations and find the solution. Label your lines clearly.
Equation 1: y = 2x - 3
Equation 2: y = -x + 3
Solution (x, y):
Show your work/calculations below:
6. A system of equations with no solution will have parallel lines when graphed.
True
False
7. The solution to a system of equations is always an integer.
True
False
8. Sarah is selling two types of handmade cards. Type A cards cost $2 each, and Type B cards cost $3 each. She sold a total of 10 cards and made $24. Write a system of two linear equations to represent this situation, then graph them to find out how many of each type of card she sold.
Let x be the number of Type A cards and y be the number of Type B cards.
Equation 1 (Total cards):
Equation 2 (Total money):
Solution (x, y):
Number of Type A cards:
Number of Type B cards:
Explain your solution: