How do I solve the system of equations by graphing? example:4x+y+2, x=
1/2+5
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To solve the system of equations by graphing, follow these steps:
1. Write down the two equations:
Equation 1: 4x + y = 2
Equation 2: x = 1/2 + 5
2. Solve each equation for y:
Equation 1: y = 2 - 4x
Equation 2: x - 1/2 = 5
To isolate x, add 1/2 to both sides:
x = 5 + 1/2
x = 10/2 + 1/2
x = 11/2
3. Create a x-y coordinate plane on a piece of graph paper.
4. Plot the points based on the two equations:
- For Equation 1, choose some values for x and calculate the corresponding y using the equation y = 2 - 4x. Plot these points on the graph.
- For Equation 2, substitute the value of x into the equation: x = 11/2. This gives us a single point on the graph.
5. Draw lines or curves connecting the plotted points for each equation.
6. Analyze the graph:
- If the lines intersect at exactly one point, it represents the solution to the system of equations.
- If the lines are parallel and do not intersect, it means there is no solution.
- If the lines overlap perfectly, it means they are the same line and have infinitely many solutions.
By following these steps, you can solve the system of equations by graphing.