Question

Y=-(1)/(3)x+2 x+3y=6 Note that you can also answer "No solution

Answer 1

To solve the given system of equations y = -1/3x + 2 and x + 3y = 6, we can use the method of substitution. This will lead to an infinite number of solutions, indicating a coinciding straight line graph.

Step-by-step explanation:

To solve the given system of equations y = -1/3x + 2 and x + 3y = 6, we can use the method of substitution.

Step 1: Substitute the value of y from the first equation into the second equation:

x + 3(-1/3x + 2) = 6

Step 2: Simplify the equation:

x - x + 6 = 6

Step 3: Combine like terms:

6 = 6

Step 4: Since the equation 6 = 6 is always true, this means that the system of equations has an infinite number of solutions. The graph of the two equations is a straight line.

Answer 2

The question involves solving two linear equations simultaneously to find a common solution. However, upon simplifying the equations, an inconsistency is found, suggesting an error in the equations or that no solution exists as the lines could be parallel.

Step-by-step explanation:

The question involves finding the solution to a system of linear equations: y = -(1/3)x + 2 and x + 3y = 6. To solve these equations simultaneously, we can either use substitution, elimination, or graphing methods to find the point of intersection of these two lines, which gives the values of x and y that satisfy both equations.

To illustrate the solution:

1. Start with the given equations:
   y = -(1/3)x + 2
   x + 3y = 6
2. Substitute the expression for y from the first equation into the second equation:
   x + 3(-1/3)x + 6 = 6
3. Simplify and solve for x:
   0x = 6
   This simplified equation suggests an error since no value of x can satisfy this equation, meaning there might be a typo in the original equations provided, or no solution exists due to parallel lines.