How do i solve this system algebraicly?
3x + 8y = 16
5x + 10y = 25
multipy the top equation by 5, the bottom by 4.
15x+40y=80
20x+40y=100
subtract the top equation frm the bottom
5x=20
go from there to solve for x, then y.
when i fill in 3(5)+ 8y = 16 it doesnt comeout even though
The Nutty Shoppe has 10 kg of mixed pecans and cashews which sell for $8.40 per kilogram. Cashews alone sell for $8 per kilogram, and pecans sell for $9 per kilogram. How many kilograms of cashews are there in the mix?
C= cashews
mixture sells 10x 8.40=$84
8c+9(10-c)
90-c=84
C=6
there are 6 kg of cashews in the mix
To solve this system of equations algebraically, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x.
3x + 8y = 16
Subtract 8y from both sides:
3x = 16 - 8y
Divide both sides by 3:
x = (16 - 8y) / 3
Step 2: Substitute the expression for x obtained in Step 1 into the second equation.
5x + 10y = 25
Substitute x with (16 - 8y) / 3:
5((16 - 8y) / 3) + 10y = 25
Step 3: Simplify and solve for y.
Multiply both sides by 3 to get rid of the fraction:
5(16 - 8y) + 30y = 75
Distribute 5 to both terms inside the parentheses:
80 - 40y + 30y = 75
Combine like terms:
80 - 10y = 75
Subtract 80 from both sides:
-10y = 75 - 80
-10y = -5
Divide both sides by -10:
y = -5 / -10
y = 1/2
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's use the first equation:
3x + 8(1/2) = 16
3x + 4 = 16
Subtract 4 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the solution to the given system of equations is x = 4 and y = 1/2.