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

2. 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

3. 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

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

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

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

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

8. 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 x
y = -4-2x
5x-2(-4-2x) = -1
5x+8+4x = -1
9x + 8 = -1
9x = -9
x = y= -4-2(-1) = -4+2 = -2
So solution is (-1,-2)

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