Review the graphs of a system of two linear equations in two variables: x - 5y = 7 and 3x - 3y + 4 Find the surullion to both equations
There seems to be a typo in the second equation you provided. It is missing an equals sign. Please provide the correct equation so that I can help you find the solution to the system of equations.
To find the solution to a system of two linear equations, we need to analyze the graphs of the given equations.
First, let's examine the first equation, x - 5y = 7.
To graph this equation, we will convert it into slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
x - 5y = 7
-5y = -x + 7
y = (1/5)x - 7/5
Now, let's determine the slope and y-intercept. The slope is 1/5, and the y-intercept is -7/5.
Plotting the graph of this equation, it will have a positive slope of 1/5 and will intersect the y-axis at -7/5.
Moving on to the second equation, 3x - 3y + 4.
Let's write it in slope-intercept form:
3x - 3y + 4 = 0
-3y = -3x - 4
y = x + 4/3
In this equation, the slope is 1, and the y-intercept is 4/3.
Plotting the graph of the second equation, it will have a positive slope of 1 and will intersect the y-axis at 4/3.
Now we can analyze the graphs of both equations together.
By inspecting the graphs individually, we see that they intersect at a single point. This single point represents the solution to the system of equations. The coordinates of this point can be determined by finding the intersection of the graphs.
Since the graphs intersect at a single point, we can conclude that there is a unique solution to this system of equations.
To find the solution to a system of two linear equations in two variables, it is helpful to graph the equations and analyze their intersection point. Let's review the given equations and their graphs.
1) x - 5y = 7:
To graph this equation, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. By rearranging the equation, we can rewrite it as y = (1/5)x - 7/5.
The graph of this equation is a line with a slope of 1/5 and a y-intercept of -7/5. To draw the line on a graph, plot the y-intercept at (0, -7/5), then apply the slope by moving upward 1 unit and to the right 5 units. Connect the points to form a line.
2) 3x - 3y + 4 = 0:
Similarly, let's rearrange this equation in slope-intercept form. Move the terms around to get y = (1/3)x + 4/3.
The graph of this equation is also a line, but it has a slope of 1/3 and a y-intercept of 4/3. Similarly, plot the y-intercept at (0, 4/3) and apply the slope to draw the line.
Now, we need to find the solution, which is the point where these two lines intersect. By observing the graph, we can see that these lines intersect at a specific point. The coordinates of this point represent the solution to the system of equations.
To find the exact values of the coordinates, we can solve the system algebraically by using substitution, elimination, or matrix methods. However, since you didn't provide the complete second equation, it is difficult to determine the exact solution.
Please double-check the second equation, and I would be happy to help you further in finding the solution.