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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 − y = 2 2x + y = 10 inconsistant(4,2)(2,3)(2,4) Q 2: Solve the system by the method of substitution 2x – 3y = –2 4x + y = 24 (4,2)(2,5)inconsistant(5,4) Q 3: Solve the system by the method of substitution x + y = 4 x - y = 2(2,1)(3,1)(1,4)inconsistant Q 4: Solve the system by the method of substitution 7x + 2y = 16 –21x – 6y = 24(13,9)(3,-4)inconsistant(4,9) Q 5: Solve the system by the method of substitution -x + 2y = 2 3x + y = 15(3,5)(2,4)(1,2)(4,3) Q 6: Solve the system by the method of substitution 2y + x = 3 4y – 3x = 1 (1,7)inconsistant(1,1)(0,2) Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!