Only people who answer correctly and answer all get brainliest and full points q1: how do you identify the solution to a system of two linear equations in two variables from their graphs? q2: what causes a system of two equations in two variables to have no solution? what causes a system of two equations in two variables to have infinitely many solutions? q3: how do you determine whether to use substitution or elimination to solve a system of equations?

Q1: The solution of a system of two linear equations in two variables is the point where their graphs intersect. At that point, the (x, y) pair satisfies both equations.

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Q2: There will be no solution when the lines representing the equations do not intersect. That will only happen when they are parallel. (We say the equations are "inconsistent.")

There will be infinitely many solutions when the lines overlap. That is, the equations for them are essentially the same equation. (We say the equations are "dependent.")

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Q3: Elimination is easiest when the coefficients of one of the variables are opposites of each other, or if one is a factor of the other. Substitution is easiest if one of the equations is easily put in the form x = ( ) or y = ( ).

If neither or both conditions hold, the choice is by student preference. (In this latter case, solution using Cramer's rule may be simplest.)

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!