Systems of Equation

Question 1

Solve a system of equations where the variable (y) does not have a coefficient in one of them

Answer 1

1. Isolate a variable (y) (preferably one w/out coefficients) in one of the equations
2. Plug in Step 1 (the value of y) into the other equation
3. Solve for x
4. Plug in value of x into one of the equations
5. Solve for y
   G: Substitute

Question 2

Solve a system of equations where a variable (x) has the same coefficient in both of the equations or can be manipulated so that both have the same coefficients

Answer 2

1. (if necessary) multiply/divide one of the equations (by a constant) so that the coefficient for the variable (x) would equal that of the other equation
2. Subtract/add one equation from the other in order to eliminate x
3. Solve for y
4. Plug in y into one of the equations
5. Solve for x
   G. Elimination

Question 3

Solve for a system of equations where the equations are ax+by=c and ax+by=d

Answer 3

No solution

*Same for ax+by=c and cax+cby=cd since dividing the 2nd by c is equal to ax+by=d

Question 4

Solve for a system of equations where the equations are ax+by=c and ax+by=c

Answer 4

Infinitely many solutions

*Same for ax+by=c and cax+cby=cc since dividing the 2nd by c is equal to ax+by=c

Question 5

1st intuitive step for any System of Equation problem

Answer 5

1. Notice if the way the equation is presented aids w/ the solving process
   1x. Notice the ways one can manipulate one of the equations to = an expressions of another equation in order to substitute the manipulated equation with the expression (and thereby, simplify the process)