Final answer:
To solve the system of linear equations, graph both lines by plotting points starting from the y-intercepts and following the slope. The intersection point of the two lines will be the solution to the system. If they don't intersect, there is no solution, and if they are the same line, there are infinite solutions.
Step-by-step explanation:
To determine the solution to the system of linear equations given by y = -2x + 4 and y = 2/3x - 4, we will graph both equations and find the point where they intersect. Linear equations are generally in the form of y = b + mx, where m represents the slope and b represents the y-intercept of the line.
For the first equation, the slope (m) is -2, and the y-intercept (b) is 4. To graph this, start at the y-intercept (0,4) on the y-axis and then use the slope to find another point. A slope of -2 means to go down 2 units for every 1 unit we move to the right. Plot another point accordingly and draw a straight line through both points.
For the second equation, the slope is 2/3 and the y-intercept is -4. Begin at the y-intercept (0,-4) and use the slope to find a second point: go up 2 units for every 3 units to the right. Plot the point and draw the line through both points.
The intersection of these two lines is the solution to the system of equations. If they intersect, plot that point; it represents the x and y values that satisfy both equations simultaneously. If the lines do not intersect, the system has no solution. If the lines overlap entirely, it means the equations represent the same line and there are infinite solutions.
Following the same example, if we consider the equation y = 9 + 3x, we would start at (0,9) and then, using the slope of 3, move up 3 units for each 1 unit to the right to find additional points for the graph.