To solve the system of equations
Y = −1/2x+4 and 3x−4y=12, we can graph both equations and find the point of intersection, which represents the solution to the system.
Let's start by graphing each equation individually:
Equation 1:
Y = −1/2 x+4
The graph of this equation is a straight line with a slope of -1/2 and a y-intercept of 4. You can plot points and draw the line.
Equation 2:
3x−4y=12
To graph this equation, we can rearrange it to slope-intercept form (y=mx+b):
4y=3x−12
y= 3/4 x−3
Now, you can plot points and draw the line.
After graphing both equations, you'll notice that the point where the two lines intersect is the solution to the system. Label this point with its coordinates. That intersection point represents the values of x and y that satisfy both equations simultaneously.
If you have a graphing tool or software, you can input the equations and plot them. Alternatively, you can plot points manually on graph paper. Once you have the graph, visually identify the point of intersection as the solution to the system.