How do you solve the system #4x - 3y = 1# and #12x - 9y = 3# by substitution?

which corresponds to the initial equation.

Replace this in the equation that follows:

Three (3) = 12x-9y = 12((3y+1)/4) -9y = 3(3y+1)-9y = 9y+3-9y = 3#

Because of this, there are an infinite number of solutions rather than enough constraints to identify a unique one.

These solutions are the locations on the line that the following equation, expressed in slope intercept form, describes:

To solve the system of equations 4x - 3y = 1 and 12x - 9y = 3 by substitution, follow these steps:

1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
5. Check the solution by substituting the values into both original equations.

Here's how to do it:

1. From the first equation, solve for x in terms of y: 4x - 3y = 1 4x = 3y + 1 x = (3y + 1)/4

2. Substitute the expression for x into the second equation: 12x - 9y = 3 12((3y + 1)/4) - 9y = 3

3. Solve the resulting equation for y: (36y + 12)/4 - 9y = 3 (36y + 12) - 36y = 12 12 = 12

4. Since 12 = 12 is always true, the equation is satisfied for all values of y. Therefore, there are infinitely many solutions.

5. To find the corresponding values of x, substitute the value of y back into one of the original equations. For example, using the first equation: 4x - 3y = 1 4x - 3(0) = 1 4x = 1 x = 1/4

So, the solution to the system is x = 1/4 and y can be any real number.