Presentation on theme: "Use the substitution method"— Presentation transcript:
1Use the substitution method EXAMPLE 1Use the substitution methodSolve the system using the substitution method.2x + 5y = –5Equation 1x + 3y = 3Equation 2SOLUTIONSTEP 1Solve Equation 2 for x.x = –3y + 3Revised Equation 2
2Use the substitution method EXAMPLE 1Use the substitution methodSTEP 2Substitute the expression for x into Equation 1 and solve for y.2x +5y = –5Write Equation 1.2(–3y + 3) + 5y = –5Substitute –3y + 3 for x.y = 11Solve for y.STEP 3Substitute the value of y into revised Equation 2 and solve for x.x = –3y + 3Write revised Equation 2.x = –3(11) + 3Substitute 11 for y.x = –30Simplify.
3Use the substitution method EXAMPLE 1Use the substitution methodThe solution is (– 30, 11).ANSWERCHECK Check the solution by substituting into the original equations.2(–30) + 5(11) –5=?Substitute for x and y.=?–30 + 3(11) 3–5 = –5Solution checks.3 = 3
4Use the elimination method EXAMPLE 2Use the elimination methodSolve the system using the elimination method.3x – 7y = 10Equation 16x – 8y = 8Equation 2SOLUTIONSTEP 1Multiply Equation 1 by – 2 so that the coefficients of x differ only in sign.3x – 7y = 10–6x + 14y = 2206x – 8y = 86x – 8y = 8
5Use the elimination method EXAMPLE 2Use the elimination methodSTEP 2Add the revised equations and solve for y.6y = –12y = –2STEP 3Substitute the value of y into one of the original equations. Solve for x.3x – 7y = 10Write Equation 1.3x – 7(–2) = 10Substitute –2 for y.3x + 14 = 10Simplify.x =43–Solve for x.
6EXAMPLE 2Use the elimination methodThe solution is ( , –2)43–ANSWERCHECKYou can check the solution algebraically using the method shown in Example 1. You can also use a graphing calculator to check the solution.
7GUIDED PRACTICEfor Examples 1 and 2Solve the system using the substitution or the elimination method.1.4x + 3y = –2x + 5y = –92.3x + 3y = –155x – 9y = 3The solution is (1,–2).ANSWERThe solution is ( , –2)3–ANSWER
8GUIDED PRACTICEfor Examples 1 and 2Solve the system using the substitution or the elimination method.3.3x – 6y = 9–4x + 7y = –16ANSWERThe solution is (11, 4)