## How many solutions can a system of 3 linear equations with 5 variables have?

(a) A homogeneous system of 3 equations in 5 unknowns. Since the system is homogeneous, it has the zero solution, hence consistent. Since there are more unknowns than equations, there are infinitely many solutions.

## How do you solve an equation with 2 variables?

Divide both sides of the equation to “solve for x.” Once you have the x term (or whichever variable you are using) on one side of the equation, divide both sides of the equation to get the variable alone. For example: 4x = 8 – 2y. (4x)/4 = (8/4) – (2y/4)

How to solve linear equations with three variables by substitution?

Solving a Linear System of Linear Equations in Three Variables by Substitution The substitution method involves algebraic substitution of one equation into a variable of the other. This will be the sample equation used through out the instructions: Equation 1)x – 6y – 2z = -8 Equation 2) -x + 5y + 3z = 2

Which is an example of the substitution method?

The substitution method involves algebraic substitution of one equation into a variable of the other. This will be the sample equation used through out the instructions: Equation 1)x – 6y – 2z = -8 Equation 2) -x + 5y + 3z = 2 Equation 3) 3x – 2y – 4z = 18 Steps in order to solve systems of linear equations through substitution:

### How to substitute equivalences in a system of equations?

You want to substitute equivalences of one of the variables into all the others—pick a variable and stick with it. To solve the following system of equations, which variable would you choose?

### Can you substitute two variables for a real number?

Substitute the value from the two variables that you solved and plug it into the remaining equation and solve for the last remaining variable. This step should allow you to solve for a real number. ü i.e.: 3 (6y + 2y – 8) – 2y – 4 (y – 6) = 18