use the Substitution Method. Please give it a try.
y = 3x + 4
5x + 3y = 12
Why is the substitution method preferred in this case?
It is relatively easy to insert 3x+4 for y in the second equation?
The substitution method is preferred in this case because one of the equations, y = 3x + 4, already gives us the value of y in terms of x. By solving for y in terms of x, we can substitute this expression into the second equation, 5x + 3y = 12, and solve for x.
To use the substitution method in this case, follow these steps:
1. Start with the given equations:
- Equation 1: y = 3x + 4
- Equation 2: 5x + 3y = 12
2. Solve the first equation for y (since it's already in terms of x):
- Substitute y = 3x + 4 into Equation 2:
5x + 3(3x + 4) = 12
3. Simplify and solve for x:
- Distribute the 3 to both terms inside the parentheses:
5x + 9x + 12 = 12
- Combine like terms:
14x + 12 = 12
- Subtract 12 from both sides:
14x = 0
- Divide both sides by 14:
x = 0
4. Substitute the value of x back into one of the original equations (e.g., Equation 1) to solve for y:
- Substitute x = 0 into y = 3x + 4:
y = 3(0) + 4
y = 4
5. Therefore, the solution to the system of equations is x = 0 and y = 4.
By using the substitution method, we were able to solve for the values of x and y that satisfy both equations in the system.