(05.02)A system of equations is shown below:x + 3y = 5 (equation 1)7x - 8y = 6 (equation 2)A student wants to prove that if equation 2 is kept unchanged and equation 1 isreplaced with the sum of equation 1 and a multiple of equation 2, the solution to thenew system of equations is the same as the solution to the original system ofequations. If equation 2 is multiplied by 1, which of the following steps should thestudent use for the proof? (4 points)

Which expressions are equivalent to -6 + 3m

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.