What are the various methods of solving systems of equations and how do we find the solutions(s)?

1-ELIMINATION.

2- SUBSTITUTION.

3- GRAPHING.

Step-by-step explanation:

Methods:

1- Elimination:

- Line up the variables.

- To cancel out one of the variables, you need to make that the coefficient of that variable opposite. For example:

As you can see, the coefficient of x in the first eqation is 3 and -3 in the second option.

- Add the equations.

- Solve for the the variable that is still present.

- Substitute the value of the variable obtained into one of the original equations.

- Solve for the other variable.

2- Substitution:

- Solve for one of the variables from any of the equations of the system.

- Substitute into the other equation for that variable.

- Solve for the other varible to find its value.

- Substitute the value obtained into any of the original equations and solve for the other variable.

3- Graphing:

- Rewrite the equations as equtions of the line slope intercept form (, where m is the slope nd b the y-intercept).

- Graph each line.

-  Then:

If there ir an intersection point of the two lines, then that point is the solution to the system

If the lines are the same, there are infinitely many  solutions.

If the lines are parallel, then there is no solution

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions