Solving systems of equations by substitution

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Presentation transcript:

Solving systems of equations by substitution Lesson 59 Solving systems of equations by substitution

substitution To be a solution to a system of equations, an ordered pair must satisfy both equations. One method for finding solutions to systems of equations is to use the substitution method

Steps for solving by substitution 1. rearrange one of the equations so that it is of the form y = mx+b or x=my+b, if necessary 2. substitute the equivalent expression for the variable from the first equation into the second equation of the system. The result is an equation with one unknown. 3.solve the resulting equation 4.substitute the value of the variable from step 3 into one of the equations to find the value of the other unknown 5. write the values of the unknowns as an ordered pair

Using substitution Solve: y = 2x-5 y= 5x+7 2x-5= 5x+7 solve -2x -2x -7 -7 -12 = 3x -4 = x y = 2(-4)-5 or y= 5(-4)+7 y = -13 y = -13 Solution is (-4,-13)

solve y= 2x-3 y= x+2 y = 4x-3 y = 3x-5

Using distributive property Solve: 12x - 6y = 12 x= -2y + 11 12x-6y=12 12(-2y+11) -6y = 12 -24y + 132 -6y = 12 -30y + 132 = 12 -30y = - 120 y = 4 x = -2(4) + 11 = 3 Solution is (3,4)

solve -5x + y = -7 y = -3x + 1 x = 3y-11 5x + 2y = -4

Rearrange before substitution If neither equation is in the form x= ? or y = ? , the first step is to rearrange one of the equations 2x+y=-4 5x-2y=-1 Rearrange the first equation 2x+y= -4 -2x -2x y = -4-2x 5x-2(-4-2x) = -1 5x+8+4x = -1 9x + 8 = -1 9x = -9 x = -1 y= -4-2(-1) = -4+2 = -2 So solution is (-1,-2)

solve 4x + 7y = 43 2x-3y = -11 2x+y = -6 3x+2y = -10 2x-3y= 8