Methods for Solving Linear Equations

When using any of the 3 methods to solve a system of linear equations the resulting solution is the same no matter which method is used.

• True; using any method will result in the correct solution.

• False; the solution varies because the solution depends on which method is used.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Identify which method for solving systems is being described by this fact: The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

• Graphing

• Substitution

• Elimination (linear combination)

6. Determine the values of x and y that satisfy the equations: 7x - 2y = 5 and 3x + 4y = 11

• x = 4, y = 3

• x = 2, y = 4

• x = 3, y = 2

• x = 5, y = 1

Determine the values of x and y that satisfy the equations: 7x - 2y = 5 and 3x + 4y = 11

• x = 4, y = 3

• x = 2, y = 4

• x = 3, y = 2

• x = 5, y = 1

Determine the values of x and y that satisfy the equations: 6x + 2y = 14 and 3x - 5y = 1

• x = 3, y = 4

• x = 2, y = 5

• x = 1, y = 7

• x = 5, y = 2

-2x+20=-5y 

• 2x+5y=20

• 2x-5y=20

• 20=2x-5y 

• -2x+5y=-20

-16x=2y-10

• 8x+y=5

• -16x-2y=10

• 16x+2y=-10

• 8x-y=-5

Find the solution to the system of equations: 4x - 3y = 5 and 2x + 7y = 1

• x = 2, y = -1

• x = -1, y = 2

• x = 5, y = 3

• x = 3, y = 4