A system of equations is a group of one or more equations with several variables. To solve a system, you must identify all of the common solutions or points of intersection.

We require at least 2 equations to solve a system of equations in 2 variables. Similarly, we will need at least 3 equations to solve a system of equations in 3 variables.

3 ways to solve a system of equations:

express y in terms of x in one of the equations and then substitute it in the 2nd equation.

- Step 1: Eliminate one of the unknowns, by multiplying equations by suitable numbers, so that the coefficients of one of the variables become the same.
- Step 2: Subtract one equation from the other to find the value of one of the unknowns.
- Step 3: Substitute the value of the found unknown into one of the original equations to calculate the second unknown value.
- Step 4: To verify the correctness of the answer, take both values and substitute them in an equation that was not used to find the value of the second unknown.

plot the graphs of simultaneous equations to get the solution.

There can be different types of solutions to a given system of equations:

- Unique solution
- No solution
- Infinitely many solutions

x = 4 + 2y

2x - 4y = 5

2(4 + 2y) - 4y = 5

8 + 4y - 4y = 5

8 = 5

Answer: The given system of equations has no solution.

Solution of a system of equations with two variables by the graphical method.

Solve and graph the system below:

x + 3y = 7

y = -2x - 1

If there are two unknowns:

Both equations are taken and brought to the "y =" state so that we could draw a graph on the coordinate line.

The intersection points of these two graphs will be the answers.

If the system has exactly one solution, then k = ( ) ?

y = x^2- x + 9

y = kx

To have exactly one solution, the discriminant = 0

Answer: k = -7 or k = 5

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