Questions: Solve the system by graphing. x+2y = 2 5x-2y = 10

Solution Steps

To solve the system of equations by graphing, we need to find the point of intersection of the two lines represented by the equations. First, we will convert each equation into the slope-intercept form (y = mx + b) to easily plot them. Then, we will use Python to graph these lines and visually identify the intersection point.

To graph the system of equations, we first convert each equation to the slope-intercept form, \( y = mx + b \).

1. For the equation \( x + 2y = 2 \): \[ 2y = -x + 2 \\ y = -\frac{1}{2}x + 1 \]

2. For the equation \( 5x - 2y = 10 \): \[ -2y = -5x + 10 \\ y = \frac{5}{2}x - 5 \]

We plot the two lines represented by the equations \( y = -\frac{1}{2}x + 1 \) and \( y = \frac{5}{2}x - 5 \) on the same coordinate plane.

The point where the two lines intersect is the solution to the system of equations. By examining the graph, we find that the lines intersect at the point \( (2, 0) \).

Final Answer