Steps for Substitution Method
The substitution method involves substituting the value of one variable expressed in terms of the other variable into the second equation:
Express y in terms of x (or vice versa) from one of the equations (preferably the simpler one).
Substitute this value of y into the other equation to get a linear equation in one variable x.
Solve for x, then substitute the value of x back to find y.
Step-by-Step Problem Solving
Solve 7x - 15y = 2 and x + 2y = 3 using Substitution
Step 1: Express x in terms of y from equation (2) x + 2y = 3:
Step 2: Substitute x = 3 - 2y in equation (1) 7x - 15y = 2:
21 - 14y - 15y = 2
21 - 29y = 2 ⟹ -29y = 2 - 21 = -19
y = 19 / 29
Step 3: Substitute y = 19/29 in Equation 3:
x = (87 - 38) / 29 = 49 / 29
Solution: x = 49/29 and y = 19/29.
Key Takeaways
Pick the equation with a coefficient of 1 or -1 to express a variable easily.
Always substitute into the other equation (never back into the same equation!).
Check your final values by substituting x and y back into both original equations.