Answer:
The solution to the system of equations is x = 2 and y = 2.
Explanation:
To solve the system of equations by graphing, we need to plot the lines represented by the equations on a coordinate plane and find the point where the lines intersect. This point represents the solution to the system of equations.
First, let's rewrite the equations in slope-intercept form (y = mx + b) to make it easier to graph them:
Equation 1: 2x + y = 6
Rearranging the equation, we get y = -2x + 6.
Equation 2: 4x = -2y + 4
Rearranging the equation, we get y = -2x - 2.
Now, we can graph the lines on a coordinate plane. Plotting a few points for each equation and connecting them with a straight line, we get:
Line 1: y = -2x + 6
Points: (0, 6) and (3, 0)
Line 2: y = -2x - 2
Points: (0, -2) and (1, -4)
By graphing the lines, we can see that they intersect at the point (2, 2). This means that the solution to the system of equations is x = 2 and y = 2.
Therefore, the solution to the system of equations is x = 2 and y = 2.