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Solving Systems of Linear Equations: Substitution Method Tutorial 14b 3 Methods to Solve There are 3 methods that we can use to solve systems of linear equations. Solve by the Graphing Method Solve by the Substitution Method Solve by the Addition (Elimination) Method Substitution Method Solve x + 3y = 7 and 2x – 4y = -6. Solve one equation for one variable. The first equation would be easiest since the x term already has a coefficient of one. x + 3y = 7 -3y -3y x = 7 – 3y 2x – 4y = -6 equation. Then solve for y. 2(7 – 3y) – 4y = -6 Substitute 2 for y in either one of the 14 – 6y – 4y = -6 two original equations to find the value 14 – 10y = -6 of the x coordinate. -14 -14 x +3(2) = 7 Step 4 is to check the 2 1 -10y = -20 answer. Click here! x+ 6 =7 y = 2 -101 x=1 1-10 Substitute 7 –3y for x in the second Substitution Method Solve x + 3y = 7 and 2x – 4y = -6. The last step is to check your solution by substituting both values, x = 1 & y = 2, in both equations. x + 3y = 7 1 +3(2) = 7 1+ 6 =7 7=7 2x – 4y = -6 2(1) – 4(2) = -6 2 – 8 = -6 -6 = -6 The solution of the system is (1, 2). Substitution Method: In Review Steps for the Substitution Method 1. Solve one equation for one of the variables. 2. Substitute the resulting expression in the other equation. Solve that equation. 3. Substitute the value of the variable from step 2 in either equation. Solve the resulting expression. 4. Check by substituting both values in both equations.