Solve by substitution method please help me solve this. I do not know how to do this at all. The question is
3x+8y=33 and x=31-6y I know that I have to plug x into the first x like 3(31-6y)+ 8y = 33 but i do not know what to do from there.
Okay so on the first side you have 3 which needs to be distributed to both the 31 and the -6y. On the left side you will end up with 93-18y+8y=33. Now you have to finish solving for y. Add 8y to -18y then subtract 93 from both sides. I think you can take it from here. Let me know if you need more help.
I do need more help...
(1)3x + 8y = 33
(2) x = 31 - 6y
when using substitution method, first you choose an equation (either of the two given) and express one of the variables in term of the other,, in this case we choose the equation (2) since x is already expressed in terms of y:
x = 31 - 6y
then substitute this to equation (1):
3(31 - 6y) + 8y = 33
93 - 18y + 8y = 33
-10y = -60
y = 6
now, substituting this value of 'y' to either equations (in this case, into equation (2)) to get x:
x = 31 - 6y
x = 31 - 6(6)
x = 31 - 36
x = -5
so there,, :)
To solve the system of equations using the substitution method, you correctly substituted the value of x into the first equation. Let's go through the steps to solve it further:
1. Start with the equation: 3(31-6y) + 8y = 33
- Distribute 3 to both terms within the parentheses: 93 - 18y + 8y = 33
- Combine like terms: 93 - 10y = 33
2. Now, let's isolate the variable y by moving constant terms to the other side of the equation:
- Subtract 93 from both sides: -10y = 33 - 93
- Simplify: -10y = -60
3. To solve for y, divide both sides of the equation by -10:
- Divide by -10: y = (-60) / (-10)
- Simplify: y = 6
Now, we have found the value of y. To find the value of x, substitute the value of y back into either of the original equations. Let's use the second equation x = 31 - 6y:
4. Substitute y = 6 into the equation x = 31 - 6y:
- x = 31 - 6(6)
- Simplify: x = 31 - 36
- Simplify further: x = -5
Therefore, the solution to the system of equations is x = -5 and y = 6.
To check your answer, plug these values back into the original equations and ensure that they satisfy both equations.