Which graph best represents this system of equations and its solution? 2x = 6 - y 5x - 4y = 28
To find which graph best represents the system of equations and its solution, let's solve the two equations:
1) 2x = 6 - y
2) 5x - 4y = 28
First, let's express both equations in terms of y:
From equation 1)
y = 6 - 2x
Now, let's manipulate equation 2) to make it look similar to equation 1):
5x - 4y = 28
-4y = 28 - 5x
y = (28 - 5x) / -4
y = -7 + (5/4)x
Now we have two equations:
y = 6 - 2x
y = -7 + (5/4)x
Let's equate these two expressions for y to find the solution for x:
6 - 2x = -7 + (5/4)x
Now, solve for x:
6 + 7 = 2x + (5/4)x
13 = (8/4)x + (5/4)x
13 = (13/4)x
x = 4
Use x to solve for y using one of the initial equations:
y = 6 - 2x
y = 6 - 2(4)
y = 6 - 8
y = -2
The solution to the system is (x, y) = (4, -2).
Based on the solution, you would look for the graph that includes both lines intersecting at the point (4, -2). Each line in the graph should correspond to the equation it represents, with appropriate slopes and y-intercepts as follows:
- The line for y = 6 - 2x starts at y-intercept (0, 6) and has a slope of -2.
- The line for y = -7 + (5/4)x starts at y-intercept (0, -7) and has a slope of 5/4.
Remember that the solution to the system is where the two lines cross, so the graph containing these two lines intersecting at the point (4, -2) is the correct representation of the system and its solution. Unfortunately, I can't visualize or provide the graph, but with the information given, you should be able to plot the lines or find the correct graph among given options.