For the following system of equations, determine how many solutions there are. y + 8 = 5x and 10x + 16 = 2y
Thank you i did it that
since they have the same slope, and can be written as
y = 5x-8
y = 5x+8
clearly the lines are parallel, so they cannot intersect
no solutions
To determine the number of solutions for the given system of equations, we can solve the system by using the method of substitution or elimination.
Let's solve it by substitution:
Step 1: Solve the first equation for y in terms of x.
y + 8 = 5x
y = 5x - 8
Step 2: Substitute the expression for y in the second equation.
10x + 16 = 2(5x - 8)
Step 3: Simplify the equation.
10x + 16 = 10x - 16
Step 4: Rearrange the equation.
10x - 10x = -16 - 16
0 = -32
Step 5: Analyze the result.
0 = -32 is a contradictory statement. This means that there are no values of x and y that simultaneously satisfy both equations.
Therefore, there are no solutions to the given system of equations.
To determine how many solutions there are for the given system of equations, we need to find the point(s) at which these two equations intersect. Let's solve the equations to find the values of x and y that satisfy both equations.
Starting with the first equation: y + 8 = 5x
Step 1: Rearrange the equation to isolate y on one side:
y = 5x - 8
Now, let's move on to the second equation: 10x + 16 = 2y
Step 2: Rearrange the equation to isolate y on one side:
2y = 10x + 16
y = 5x + 8
We now have two equations in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Comparing the two equations, we observe that they have the same slope but different y-intercepts. The slope of both equations is 5, indicating that the lines are parallel.
Since parallel lines do not intersect, there are no common points of intersection for the two equations. Therefore, there are no solutions to this system of equations.
In summary, there are no solutions to the given system of equations since the two equations represent parallel lines that do not intersect.