I need help! I am confused! Algebra
solve using substitution or elimination.10x-15y=10 4x+6y=0
10x-15y=10, 4x+6y=0
First I would reduce the equations
10x - 15y = 10 ---> 2x - 3y = 2
4x + 6y = 0 -----> 2x + 3y = 0
Of course the easiest way from here would be to add them
that is, using elimination, BUT ...
you wanted substitution, so form the first 2x = 2 + 3y
sub that into the 2nd
2x + 3y = 0
2 + 3y + 3y = 0
6y = -2
y = -1/3
sub back into 2x = 2 + 3y
2x = 2 + 3(-1/3) = 1
x = 1/2
Thank You! 👍🏻
Scooter Fun and Skoot Zoom are electronic scooter rental companies.
Scooter Fun charges a $15 deposit plus $5 per hour rental fee.
Skoot Zoom charges a $10 deposit plus $10 per hour rental fee.
The system of equations represents the cost, y, for renting a scooter for x hours.
y = 5x + 15
y = 10x + 10
What is the solution to the system of equations? Type your answer as an ordered pair. What does it mean in the context of this problem?
To solve the system of equations using substitution or elimination, we will eliminate one variable and then substitute the value into the other equation. Let's go step by step:
1. Elimination method:
In the given equations:
Equation 1: 10x - 15y = 10
Equation 2: 4x + 6y = 0
We can multiply Equation 2 by 5 to make the coefficients of 'y' the same, allowing us to eliminate 'y' when we add the two equations:
Multiply Equation 2 by 5: 20x + 30y = 0
Now, add Equation 1 and Equation 2:
(10x - 15y) + (20x + 30y) = 10 + 0
30x + 15y = 10
Now, divide the entire equation by 15 to simplify it:
2x + y = (10/15)
2x + y = 2/3
2. Substitution method:
In Equation 2, solve for 'x' in terms of 'y':
4x = -6y
x = (-6y)/4
x = -3y/2
Substitute this value of 'x' into Equation 1:
10(-3y/2) - 15y = 10
-15y/2 - 15y = 10
-15y - 30y = 20
-45y = 20
Divide both sides of the equation by -45 to solve for 'y':
y = 20/(-45)
y = -4/9
Now, substitute the value of 'y' back into Equation 2 to solve for 'x':
4x + 6(-4/9) = 0
4x - 24/9 = 0
4x = 24/9
x = (24/9)/4
x = 2/3
Therefore, the solution is x = 2/3 and y = -4/9.