solve the system by graphing. Then classify 2x-y=12 2x+3y=4. Thank you
To solve the system of equations by graphing, we need to plot the equations on a coordinate plane and find the point of intersection.
First, let's rewrite the equations in slope-intercept form, which is y = mx + b, where "m" represents the slope and "b" represents the y-intercept.
Equation 1: 2x - y = 12
Rearranging the equation, we get:
-y = -2x + 12
Dividing by -1, the equation becomes:
y = 2x - 12
Equation 2: 2x + 3y = 4
Rearranging the equation, we get:
3y = -2x + 4
Dividing by 3, the equation becomes:
y = (-2/3)x + 4/3
Now, let's plot these equations on a graph:
Equation 1: y = 2x - 12
To plot this equation, start by plotting the y-intercept, which is -12. Then use the slope (2/1) to plot additional points. From the first point, move up 2 units and right 1 unit to plot the second point. Connect these two points with a straight line.
Equation 2: y = (-2/3)x + 4/3
Start by plotting the y-intercept, which is 4/3. Then use the slope (-2/3) to plot additional points. From the initial point, move down 2 units and right 3 units to plot the second point. Connect these two points with a straight line.
After plotting these equations, we can now identify the point of intersection. That point is the solution to the system of equations.
Once you have graphed the equations, look for the point where the two lines intersect. If there is an intersection point, it means there is a solution to the system. If there is no intersection point or the lines are parallel, it means there is no solution.
By analyzing the graph, we can see that the lines intersect at a single point: (-2, -16/3).