FIERY SUBSTITUTION
| STEP 1 : SOLVE ONE OF THE EQUATIONS FOR ITS VARIABLES. |
| STEP 2 : SUBSTITUTE THE EXPRESSION FROM STEP 1 INTO THE OTHER EQUATION AND SOLVE FOR THE OTHER VARIABLE |
| STEP 3 : SUBSTITUTE THE VALUE FROM STEP 2 INTO THE REVISED EQUATION FROM STEP 1 AND SOLVE. |
EXAMPLE
3x + 4y =-4 , x + 2y = 2
1. SOLVE EQUATION 2 FOR x
x + 2y = 2 write equation 2
x = -2y +2 revised equation 2
2. SUBSTITUTE THE EXPRESSION FOR x INTO EQUATION 1 AND SOLVE FOR y.
3x + 4y =-4 write equation 1
3( -2y +2 ) + 4y =-4 substitute -2y + 2 for x
y =5 solve for y
3. SUBSTITUTE THE VALUE OF y INTO THE REVISED EQUATION 2 AND SOLVE FOR x
x = -2y + 2 write revised equation 2
x = -2( 5 ) + 2 substitute 5 for y
x = -8 simplify
THE SOLUTION IS ( -8, 5)
CHECK CHECK THE SOLUTION BY SUBSTITUTING BACK INTO THE ORIGINAL PROBLEMS
3x + 4y = -4 write original equations x + 2y = 2
3(-8) + 4(5) = -4 substitute for x and y -8 + 2(5) = 2
-4 = -4 solution checks 2 = 2