review the graphs of a system of two linear equations in two varibles: x-5y=7 and 3x-2y=-4. find the solution to both equations
To find the solution to both equations, we first need to graph the system of two linear equations.
1. x - 5y = 7
Rearranging the equation to y = mx + b form, we get:
-5y = -x + 7
y = (1/5)x - 7/5
2. 3x - 2y = -4
Rearranging the equation to y = mx + b form, we get:
-2y = -3x - 4
y = (3/2)x + 2
Now let's graph both equations on the same coordinate system:
The graph of the first equation (red line):
- Plot the y-intercept at (0, -7/5).
- Use the slope of 1/5 to plot a second point and draw the line through the two points.
The graph of the second equation (blue line):
- Plot the y-intercept at (0, 2).
- Use the slope of 3/2 to plot a second point and draw the line through the two points.
Upon plotting the two lines, we see that they intersect at the point (1, -2). Therefore, the solution to the system of equations is x = 1 and y = -2.