solve this system of equation using the substitution method.
6x+8y=72
2x+5y=45
multiply the 2nd by 3 and subtract to solve for y
then sub that back into the original 2nd to get x.
I am sure you can do it.
To solve this system of equations using the substitution method, we will solve one of the equations for one variable and then substitute that expression into the other equation.
Let's solve the first equation for x:
6x + 8y = 72
Rearrange the equation to isolate x:
6x = 72 - 8y
x = (72 - 8y) / 6
x = 12 - (4/3)y
Now we substitute this expression for x in the second equation:
2x + 5y = 45
Replace x with (12 - (4/3)y):
2(12 - (4/3)y) + 5y = 45
24 - (8/3)y + 5y = 45
Multiply through by 3 to get rid of the fraction:
72 - 8y + 15y = 135
Combine like terms:
7y = 63
Divide both sides by 7:
y = 9
Now that we have found the value of y, we can substitute it back into the first equation to find the value of x:
6x + 8(9) = 72
6x + 72 = 72
Subtract 72 from both sides:
6x = 0
Divide both sides by 6:
x = 0
Therefore, the solution to the system of equations is x=0 and y=9.