8x -5y =20
5y -8x=-20
x= -4
Solve the system of equations by graphing.
Check this problem for me.
Your first two equations are not independent. One can be derived from the other. Ordinarily, this would imply that there are an infinite number of solutions.
However, your last equation tells you what x is. Did you derive that equation or was it provided? You can use x = -4 and either of the first two equations to compute y.
-32 - 5y = 20
5y = -52
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To solve the system of equations by graphing, we need to graph each equation and find the point of intersection.
Let's graph the first equation, 8x - 5y = 20:
Step 1: Convert the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
8x - 5y = 20
-5y = -8x + 20
y = (8/5)x - 4
Step 2: Plot the y-intercept, which is -4. Start at the point (0, -4).
Step 3: Use the slope to find another point. The slope in this case is 8/5, which means for every 5 units we move to the right, we move up 8 units. So, from the intercept point (0, -4), move 5 units to the right and 8 units up, giving us the point (5, 4).
Step 4: Draw a straight line passing through the two points. This line represents the first equation.
Now let's graph the second equation, 5y - 8x = -20:
Step 1: Convert the equation into slope-intercept form (y = mx + b).
5y - 8x = -20
5y = 8x - 20
y = (8/5)x - 4
Step 2: Plot the y-intercept, which is -4. Start at the point (0, -4).
Step 3: Use the slope to find another point. The slope is the same as the first equation, 8/5. From the intercept point (0, -4), move 5 units to the right and 8 units up, giving us the point (5, 4).
Step 4: Draw a straight line passing through the two points. This line represents the second equation.
Now, look for the point of intersection of the two lines. In this case, it seems that the two equations are identical. They represent the same line. So, they intersect at infinitely many points, and any point on the line satisfies both equations.
Therefore, the solution to the system of equations is any point on the line represented by the equation 8x - 5y = 20 or 5y - 8x = -20.
To check if x = -4 is a solution, substitute x = -4 into either of the equations and check if it satisfies the equation. Let's use the first equation:
8x - 5y = 20
8(-4) - 5y = 20
-32 - 5y = 20
-5y = 52
y = -10.4
So, when x = -4, y = -10.4. Therefore, the point (-4, -10.4) lies on the line.
Therefore, x = -4 is a valid solution.