Graph this system of equations and determine the number of solutions.y=13xy=–13x+4Click to select points on the graph.-10-8-6-4-2246810-10-8-6-4-2246810xyy=13xy=–13x+4How many solutions does the system of equations have?infinitely many solutionsno solutionone solutionSubmit
Question
Graph this system of equations and determine the number of solutions.y=13xy=–13x+4Click to select points on the graph.-10-8-6-4-2246810-10-8-6-4-2246810xyy=13xy=–13x+4How many solutions does the system of equations have?infinitely many solutionsno solutionone solutionSubmit
Solution
To graph the system of equations and determine the number of solutions, follow these steps:
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Start by understanding the equations. You have two equations here: y = 13x and y = -13x + 4.
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Graph the first equation, y = 13x. This is a straight line that passes through the origin (0,0) and has a slope of 13. This means for every unit increase in x, y increases by 13 units.
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Graph the second equation, y = -13x + 4. This is also a straight line. It has a y-intercept at (0,4) (where the line crosses the y-axis) and a slope of -13. This means for every unit increase in x, y decreases by 13 units.
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Look for the point(s) where the two lines intersect. This point represents the solution to the system of equations.
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If the lines intersect at one point, then there is one solution to the system of equations. If the lines are parallel and never intersect, then there is no solution. If the lines coincide (i.e., they are the same line), then there are infinitely many solutions.
In this case, the two lines are parallel and do not intersect, so there is no solution to the system of equations.
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