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 review the graphs of a system of two linear equations, we can find the x and y-intercepts of each equation and plot them on a graph.
Equation 1: x - 5y = 7
To find the x-intercept, we set y = 0:
x - 5(0) = 7
x = 7
So, the x-intercept is (7, 0).
To find the y-intercept, we set x = 0:
0 - 5y = 7
-5y = 7
y = -7/5
So, the y-intercept is (0, -7/5).
Equation 2: 3x - 2y = -4
To find the x-intercept, we set y = 0:
3x - 2(0) = -4
3x = -4
x = -4/3
So, the x-intercept is (-4/3, 0).
To find the y-intercept, we set x = 0:
3(0) - 2y = -4
-2y = -4
y = 2
So, the y-intercept is (0, 2).
Now, we can plot these points on a graph:
(7, 0) and (0, -7/5) for the first equation, and
(-4/3, 0) and (0, 2) for the second equation.
The graph of the first equation (in blue) is a line passing through (7, 0) and (0, -7/5):
https://www.desmos.com/calculator/9w0y8zpkq0
The graph of the second equation (in red) is a line passing through (-4/3, 0) and (0, 2):
https://www.desmos.com/calculator/3ocdqgfnqo
The solution to the system of equations is the point where these two lines intersect on the graph. By looking at the graphs, we can see that the point of intersection is approximately (2, -1). Therefore, the solution to both equations is x = 2 and y = -1.