explain how you solve 11x=3y=12 using 3x=9 as subsitution
I have a feeling you meant:
11x + 3y = 12 (the + and = are the same key)
for 3x = 9 ---> x = 3
then ...
11(3) + 3y = 12
3y = 12-33
3y = -21
y = -7
x = 3 , y = -7
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To solve the equation 11x + 3y = 12 using the substitution method with the equation 3x = 9, follow these steps:
Step 1: Solve the equation 3x = 9 for x.
- Divide both sides of the equation by 3: 3x/3 = 9/3.
- This simplifies to x = 3.
Step 2: Substitute the value of x into the first equation.
- Replace x with 3 in the equation 11x + 3y = 12.
- This gives: 11(3) + 3y = 12.
Step 3: Solve the resulting equation for y.
- Multiply 11 by 3 and simplify: 33 + 3y = 12.
- Subtract 33 from both sides of the equation: 3y = 12 - 33.
- Simplify to get: 3y = -21.
- Divide both sides of the equation by 3: (3y)/3 = (-21)/3.
- This simplifies to y = -7.
Step 4: Solution Check.
- Substitute the values of x and y into the original equations to verify.
- For the equation 11x + 3y = 12: 11(3) + 3(-7) = 12.
- Simplify: 33 - 21 = 12.
- The equation holds true, so the values x = 3 and y = -7 are the solution to the system of equations.
Therefore, the solution to the system of equations 11x + 3y = 12 and 3x = 9 using substitution is x = 3 and y = -7.