Systems of Equations
3 different types of Systems
Name______________ Period____
1) Both equations are in slope-intercept form (y = a + bx) use substitution.
Set the two equations equal to each other and
solve for x. Then substitute x back into both
equations.
Example:
y = -5 + 3x and y = -9 + 5x
-5 + 3x = -9 + 5x
Graph each equation.
a=y-intercept and b=slope
subtract 3x
-5 = -9 + 2x
add 9
4 = 2x
divide by 2
x=2
then y = 3(2) – 5 and y = 5(2) -9
y=1
and y= 1
The solution is (2,1)
Solve: y = 7 – 2x and y = 6x - 1
Graph each equation
Solve: y = 3x + 5 and y = 4x + 8
Graph each equation
2. If one equation is in slope intercept form and the other equation is in standard form use
substitution.
Substitute one equation into the other equation.
To check graphically solve for y
2x -3y = 14
Subtract 2x
-3y = 14 – 2x
Divide by -3
y = -14/3 + 2x/3
Example:
y = x – 2 and 2x – 3y = 14
plug x – 2 in for y
2x – 3(x – 2) = 14
Do the distributive property
2x – 3x + 6 =14
Combine like terms
-x + 6 = 14
Subtract 6 from both sides
-x = 8
Multiply by -1
x = -8
Find y
y = -8 -2
y= -10
The solution is (-8, -10)
Solve: y = 2x – 3 and x – y = -4
Graph each equation
Solve x = 4 – 2y and 3y – x = 6
Graph each equation
3. If both equations are in standard form use the elimination method.
The elimination method
Example
can be used to solve a
2x + 3y = 10
system of linear equations.
3x – 4y = -2
By adding the two linear
Multiply the top equation by 4 and the bottom by 3.
equations in a way that
8x + 12y = 40
eliminates one of the
9x – 12y = -6
variables, a single variable Add the two equations together vertically. (y is eliminated)
equation is left.
17x = 34 Divide by 17
x=2
Find y, substitute x into an equation
2(2) + 3y = 10
4 + 3y = 10
3y = 6
y=2
The solution is (2,2) Check by substituting x =2 and y = 2 into both
equations.
2(2) + 3(2) = 10
and
3(2) – 4(2) = -2
4 + 6 = 10
6 - 8 = -2
10 = 10
-2 = -2
Example:
2x + y = 4
3x – y =16
Example:
3x + 2y = -39
x+y=4
Practice:
2x + 5y = 1
-2x + y = -19
Practice:
x + 3y = 4
4x – 6y = 1
Example:
3x – 10y = 16
-4x – 8y = 0
Practice:
5x + 6y = 16
3x – 4y = 2