Review the graphs of a system of two linear equations in two variables: X - 5y = 7 and 3x - 2y = -4
Find the solution to both equations.
To find the solution to the system of equations, we can either graph the equations and find the point of intersection or use the method of substitution or elimination.
Let's start by graphing the equations:
For the equation X - 5y = 7, we can rewrite it in slope-intercept form as y = (1/5)x - 7/5. We can plot this equation on a graph:
-5 | -2
0 | -7/5
5 | -6/5
For the equation 3x - 2y = -4, we can rewrite it in slope-intercept form as y = (3/2)x + 2. We can plot this equation on the same graph:
-2 | -5
0 | 2
4/3 | 4
The two lines intersect at the point (2, -1). Therefore, the solution to the system of equations is x = 2 and y = -1.