9.2 Systems of Equations

Question 1

how to prove whether values of x,y and z is a solution to three systems of equations?

Answer 1

plug the values of x,y and z into the systems, if both sides equal one another in every equation, this proves that the values are a solution

Question 2

how to solve systems of equations using substitution?

Answer 2

1. isolate for one to the variables
2. pull the value of the variable into the other equation to find the value of one variable
3. plug the value of the variable into another equation to find the value of the other variable
4. state the coordinate given the x and y values

Question 3

how to tell if two systems are parallel?

Answer 3

if their equations are the same or scalar multiples of one another

Question 4

how to determine a linear equation given parametric equations?

Answer 4

1. write the vector equation
2. find a point when multiplied to the direction vector will give 0 otherwise known as the normal to the point
3. plug coordinates into the equation n1x+n2y+c=0 and solve for c value
4. write the equation with the c value

Question 5

when do two systems have no solutions?

Answer 5

when they are parrallel

Question 6

when does a system of equation have infinite solutions?

Answer 6

when both equations are multiples of each other, they have have an infinite amount of solutions because they are coincident

Question 7

what does the solution in a system of equations mean?

Answer 7

means the point works for both equations

Question 8

What is Linear equation form?

Answer 8

Ax+By+C=0