hi friends, i have another question that i could use some help on for my semester exam.
how many solutions does this system of equations have?
3x + 15y =35 and y= -1/5x + 7/3
i hate these kinds of probloms and could really use some help
putting the 1st equation into slope-intercept form
... 15y = -3x + 35 ... y = -1/5 x + 7/3
the equations are the same
... so the possible number of system solutions is infinite
OH i see thank YOU!!!!
Of course, I'm here to help. Let's start by solving the system of equations step by step.
The given system of equations is:
1) 3x + 15y = 35
2) y = -1/5x + 7/3
We can solve this system of equations using substitution or elimination method. Let's use substitution.
Step 1: Solve equation 2) for y in terms of x.
y = -1/5x + 7/3
Step 2: Substitute the value of y from equation 2) into equation 1).
3x + 15(-1/5x + 7/3) = 35
Step 3: Simplify the equation.
3x - 3x/5 + 35 = 35
Step 4: Combine like terms.
-3x/5 + 35 = 35
Step 5: Subtract 35 from both sides of the equation.
-3x/5 = 0
Step 5: Multiply both sides of the equation by 5.
-3x = 0
Step 6: Divide both sides of the equation by -3.
x = 0
Step 7: Substitute the value of x into equation 2) to find y.
y = -1/5(0) + 7/3
y = 7/3
So, the solution to the system of equations is x = 0 and y = 7/3.
Since we have found a unique solution for both x and y, the system of equations has only one solution.
Hello! I'd be happy to help you with your question on the number of solutions for the given system of equations.
To determine the number of solutions, we need to analyze the relationship between the two equations. The given system consists of two linear equations:
1) 3x + 15y = 35
2) y = (-1/5)x + 7/3
The second equation is already in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. Let's compare the slopes of the two equations:
1) The first equation can be rewritten as: 15y = -3x + 35.
Divide both sides by 15: y = (-3/15)x + 35/15, which simplifies to y = (-1/5)x + 7/3.
Comparing the slopes between the two equations, we see that both equations have the same slope, which is -1/5. This means that the two lines are parallel to each other.
When two lines are parallel, they will never intersect and thus will not have any points in common. Therefore, there are no solutions to the given system of equations.
In summary, the system of equations has no solution.
I hope this explanation helps you understand how to determine the number of solutions for a system of equations. If you have any further questions, feel free to ask!