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### High School Mathematics1.21 Linear Equations in Two Variables- Solving by the Method of Substitution

 Method: Solve one of the equations for one variable in terms of the other. Substitute that expression found in step 1 into the other equation to obtain an equation in one variable. Solve the equation obtained in step 2 Back substitute the solution in step 3 into the expression obtained in step 1 to find the value of the other variable Check that the solution satisfies each of the original equations Example: Solve the same system of equations by the method of substitution. 2x + y = 4 ----- Equation 1 x − y = −1 ------- Equation 2 Solution: Take equation 1: 2x + y = 4 ----- Equation 1 2x + y = 4 y = 4 - 2x Substituting y in equation 2 x − y = −1 ------- Equation 2 x − (4 − 2x) = −1 Solving for x x − 4 + 2x = −1 3x = −1 + 4 3x = 3 x = 1 To find y, substitute x = 1 in equation 1 2x + y = 4 ----- Equation 1 2x + y = 4 2(1) + y = 4 2 + y = 4 y = 4 - 2 y = 2 x = 1 and y = 2 Answer: (1,2) Directions: Solve the linear equations by the method of substitution. Also write at least 5 examples of your own.
 Q 1: Solve the system by the method of substitution x - 3y = -2 5x + 3y = 17(4/3,5/3)(1/2.2/3)(5/2,3/2)inconsistant Q 2: Solve the system by the method of substitution 2x – 3y = –2 4x + y = 24 (2,5)(4,2)inconsistant(5,4) Q 3: Solve the system by the method of substitution 2x + y = 6 -x + y = 0(1,0)(2,3)(4,2)(2,2) Q 4: Solve the system by the method of substitution x + y = 4 x - y = 2inconsistant(3,1)(1,4)(2,1) Q 5: Solve the system by the method of substitution 7x + 2y = 16 –21x – 6y = 24(3,-4)(13,9)inconsistant(4,9) Q 6: Solve the system by the method of substitution -x + 2y = 2 3x + y = 15(1,2)(3,5)(4,3)(2,4) Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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