Solve the system of linear equations by graphing. Round the solution to the nearest tenth as needed.y+2.3=0.45x−2y=4.2x−7.8Responses(2.4,−1.2)2 point 4 comma negative 1 point 2(−1, 2.5)negative 1 comma 2 point 5infinitely many solutionsinfinitely many solutionsno solution
Question
Solve the system of linear equations by graphing. Round the solution to the nearest tenth as needed.y+2.3=0.45x−2y=4.2x−7.8Responses(2.4,−1.2)2 point 4 comma negative 1 point 2(−1, 2.5)negative 1 comma 2 point 5infinitely many solutionsinfinitely many solutionsno solution
Solution
To solve the system of linear equations by graphing, follow these steps:
- Rewrite each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
The first equation is already in this form: y = 0.45x - 2.3
The second equation can be rewritten as: y = 4.2x - 7.8
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Graph each equation on the same set of axes.
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Look for the point where the two lines intersect. This point is the solution to the system of equations.
If the lines intersect at a single point, then there is one solution to the system of equations, and the coordinates of the point of intersection are the solution.
If the lines are parallel and do not intersect, then there is no solution to the system of equations.
If the lines coincide (are the same line), then there are infinitely many solutions to the system of equations.
Without graphing the equations, it's impossible to determine the exact solution. However, you can see that the slopes of the two lines are different (0.45 vs 4.2), so the lines are not parallel and do not coincide. Therefore, there should be a single solution to the system of equations.
To find the exact solution, you would need to graph the equations or use a method such as substitution or elimination.
Similar Questions
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