raph the first equation y = 1/2x + 5 by starting at (0,5) and following the slope of 1/2. Graph the second equation 2x + 3y = -6 (rewritten as y = -2/3x - 2) by starting at (0,-2) with a slope of -2/3. The intersection of these lines on the graph is the solution to the system.
To graph the system of linear equations and identify the solution, first plot each equation on the graph using Desmos or a similar graphing tool.
The first equation, y = 1/2x + 5, has a slope of 1/2 and a y-intercept of 5.
To graph this line, you would start at the point (0,5) on the y-axis and then rise 1 unit for every 2 units you move to the right along the x-axis.
For the second equation, 2x + 3y = -6, you can rearrange it into slope-intercept form (y = mx + b) to get: y = -2/3x - 2.
This line has a slope of -2/3 and a y-intercept of -2.
Start at the point (0,-2) and from there, for every 3 units you move to right along the x-axis, you would go down 2 units.
The intersection point of these two lines on the graph gives the solution to the system of linear equations.
This is the point where both equations have the same x and y values, which is the solution to the system.