You can't. Math is not an algebraic expression. Simplifying an equation, however, can take multiple forms. Sometimes simplify simply means to solve an equation. Other times, it can mean to bring an equation into a standard form, such as with line equations, or quadratic equations.
Well, that depends on what you mean "solve by factoring." For any quadratic equation, it is possible to factor the quadratic, and then the roots can be recovered from the factors. So in the very weak sense that every quadratic can be solved by a method that involves getting the factors and recovering the roots from them, all quadratic equations can be solved by factoring. However, in most cases, the only way of factoring the quadratic in the first place is to first find out what its roots are, and then use the roots to factor the quadratic (any quadratic polynomial can be factored as k(x - r)(x - s), where k is the leading coefficient of the polynomial and r and s are its two roots), in which case trying to recover the roots from the factors is redundant (since you had to know what the roots were to get the factors in the first place). So to really count as solving by factoring, it makes sense to require that the solution method obtains the factors by means that _don't_ require already knowing the roots of the polynomial. And in this sense, most quadratic equations are not solvable through factoring.
algebra involves equations with numbers a variables and your goal is to solve for the variable
Do you mean "equations involving exponential functions"? Yes,
basically it means an answer for a multiplication problem
Find values for each of the unknown variables (or at least as many as is possible for the system) that satisfy all the equations.
You can't. Math is not an algebraic expression. Simplifying an equation, however, can take multiple forms. Sometimes simplify simply means to solve an equation. Other times, it can mean to bring an equation into a standard form, such as with line equations, or quadratic equations.
The answer depends on what you mean by shapes. These curves are not closed shapes.
Finding a set of value for the set of variables so that, when these values are substituted for the corresponding variables, all the equations in the system are true statements.
Well, that depends on what you mean "solve by factoring." For any quadratic equation, it is possible to factor the quadratic, and then the roots can be recovered from the factors. So in the very weak sense that every quadratic can be solved by a method that involves getting the factors and recovering the roots from them, all quadratic equations can be solved by factoring. However, in most cases, the only way of factoring the quadratic in the first place is to first find out what its roots are, and then use the roots to factor the quadratic (any quadratic polynomial can be factored as k(x - r)(x - s), where k is the leading coefficient of the polynomial and r and s are its two roots), in which case trying to recover the roots from the factors is redundant (since you had to know what the roots were to get the factors in the first place). So to really count as solving by factoring, it makes sense to require that the solution method obtains the factors by means that _don't_ require already knowing the roots of the polynomial. And in this sense, most quadratic equations are not solvable through factoring.
algebra involves equations with numbers a variables and your goal is to solve for the variable
Do you mean "equations involving exponential functions"? Yes,
It probably means that one of the equations is a linear combination of the others/ To that extent, the system of equations is over-specified.
If you mean 3x2+4x-2 = 0 then it can be solved by means of the quadratic equation formulla
If you mean x+2y = -2 and 3x+4y = 6 then the solutions to the equations are x = 10 and y = -6
basically it means an answer for a multiplication problem
this means you have no more than 5 solutions in a system of equations.