EIV

Question 1

Whether 2 equations involving 2 variables will be sufficient to solve for the variables

Answer 1

If both equations are linear - that is if there are no squared terms and no (xy) terms - the equations will be sufficient unless the two equations are mathematically identical

Question 2

Whether 2 equations involving 2 variables will be sufficient to solve for the variables

Answer 2

If there are any non-linear terms in either of the equations (x^2, xy, or x/y), there will usually be two (or more) different solutions for each of the variables and the equations will not be sufficient

Question 3

x² - y² =

Answer 3

(x+y) (x-y)

Question 4

x² + 2xy + y² =

Answer 4

(x+y) (x+y)

Question 5

x² - 2xy +y² =

Answer 5

(x-y) (x-y) or (x-y)²

Question 6

a² - 1 =

Answer 6

(a+1) (a-1)

Question 7

Inequalities: When dividing or multiplying by a negative number…

Answer 7

…the inequality sign flips

Question 8

4 - 3x < 10 =

Answer 8

x > 2

Question 9

Inequalities: You should never…

Answer 9

…subtract or divide inequalities

Question 10

Inequalities: You can only…

Answer 10

multiply when you know both variables are positive

Question 11

3 x LT8 =

Answer 11

LT24

Question 12

8 + LT2 =

Answer 12

LT10

Question 13

8 - LT2 =

Answer 13

GT6

Question 14

6 x LT3 =

Answer 14

LT18

Question 15

-6 x LT3 =

Answer 15

GT-18

Question 16

8 / LT2* =

Answer 16

GT4 *If we know LT2 is positive

Question 17

Square roots: You cannot…

Answer 17

…square root a negative number