The graph of the system of equations −2x + y = 3 and 4x + 2y = 2 is a straight line that intersects the x-axis at the point (1,0) and the y-axis at the point (0,3).
To see this, we can solve the system of equations by elimination method. First, we can multiply the second equation by -2 to obtain the following system:
−2x + y = 3
-8x - 4y = -4
Then, we can add the two equations to eliminate the y-term:
(-8x - 4y) + (-2x + y) = -4 + 3
-10x - 3y = -1
Solving for x, we get x = 1/5. Substituting this value back into either of the original equations, we can solve for y:
−2x + y = 3
−2(1/5) + y = 3
y = 3
Therefore, the solution to the system of equations is (1/5, 3). The graph of the system is a straight line that passes through the point (1/5, 3).
The x-intercept of the line is the point at which it crosses the x-axis, which is the point (1,0). The y-intercept of the line is the point at which it crosses the y-axis, which is the point (0,3).
Overall, the graph of the system of equations is a straight line that intersects the x-axis at the point (1,0) and the y-axis at the point (0,3).