7.1, 2 And 3

Front 1

System of linear equations (7.1)

Back 1

Two or more linear equations in the same variables.
AKA a "linear system"

EX: x+2y=7 and 3x-2y=5

Front 2

Solution of a system of linear equations (7.1)

Back 2

An ordered pair that satisfies each equation in the system.
AKA the place where the two lines intersect

Front 3

Solving a linear system (7.1)

Back 3

1. Graph both equations
2. Estimate the point of intersection
3. Check whether the ordered pair is a solution for both equations by substituting x and y

Front 4

Solving a linear system using the substitution method (7.2)

Back 4

1. Solve one of the equations for one of its variables
2. Substitute the expression from Step 1 into the other equation and solve for the other variable
3. Substitute the value from Step 2 into the revised equation from Step 1 and solve

EX: y = 3x + 2 and x + 2y = 11
1. Solve for a variable -- y = 3x + 2 is already solved for y
2. Substitute 3x + 2 for y in equation 2 and solve for x -- x + 2 (3x + 2) = 11, ergo x = 1
3. Substitute 1 for x in the original Equation 1 to find the value of y -- y = 3x + 2 = 3 (1) + 2 = 5

The solution is (1,5)

Front 5

Solving a linear system by adding or subtracting (7.3)

Back 5

1. Add or subtract the equations to eliminate one variable
2. Sole the resulting equation for the other variable
3. Substitute in either original equation to find the value of the eliminated variable

EX: 2x + 3y = 11 and -2x + 5y = 13
1. Add the equations to eliminate one variable
(2x + 3y = 11)
+(-2x + 5y = 13)
= 8y = 24
2. Solve for y
y = 3
3. Substitute 3 for y in either equation and solve for x
2x + 3 (3) = 11
x=1
The solution is (1,3)