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Gives an example and how to solve it.

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The graphing method on graph paper can be useful when the intersection point happens to have integer coordinates (as seen in the example above). It becomes less helpful, however, when the coordinates are not integers. If it appears that the intersection point does not lie on the intersection of the grids of the graph paper, try an algebraic solution method or grab your graphing calculator.

In addition to solving systems of equations algebraically, you can also solve them graphically. A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator.

Graphical Method - on graph paper

Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the ( x,y) ordered pair where the two lines intersect (cross).

Solve this system of equations graphically and check your solution: (
easy one)

y = 2x + 1 and y = -x + 7

Identify the slope and 1. The equations in this example are already set equal to "y".y-intercept in each equation. Remember: y = mx + b, where m = slope and b = y-intercept.

slope = -1 y = - x + 7
y-intercept = 7

2. Graph the lines.

Find the intersection point (where the lines cross). This means the solution to this system is:Solution:
These lines cross at the point (2,5).

x = 2 and y = 5.

Substitute 3. CHECK: x = 2 and y = 5 into BOTH of the original equations. If your solutions are correct, both equations will be true!

) + 1 y = 2 x + 1
5 = 2( 2 (check)
5 = 5

) + 7 y = - x + 7
5 = -( 2(check)
5 = 5

Two special cases!

Solve system: y = 2x + 4 and y = 2x - 2 Solution: No solution

Solve system: y = -2x + 1 and 2x + y = 1 Solution: Infinite number of solutions

Solve this system of equations graphically and check your solution: (
harder one)

x = y + 1 and 2 x + y = -7

Set the equations equal to 1. y to make graphing easier.

Identify the slope and 2. y-intercept in each equation.

slope = 1 y = x - 1
y-intercept = -1

slope = -2 y = -2
y-intercept = -7 x - 7

Find the intersection point (where the lines cross). This means the solution to this system is:
These lines cross at the point (-2,-3).

x = -2 and y = -3.

Substitute 4. CHECK: x = -2 and y = -3 into BOTH of the original equations. If your solutions are correct, both equations will be true!

x = y + 1
-2 = -3 + 1
-2 = -2 (check)

2) = -7 x + y = -7 2( -2 ) + ( -3 (check)
-4 + (-3) = -7
-7 = -7

Graphical Method - graphing calculator

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Systems of Linear Equations - Graphical Solution - MathBitsNotebook(A1 - CCSS Math)

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The graphing method on graph paper can be useful when the intersection point happens to have integer coordinates (as seen in the example above). It becomes less helpful, however, when the coordinates are not integers. If it appears that the intersection point does not lie on the intersection of the grids of the graph paper, try an algebraic solution method or grab your graphing calculator.

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Solves the equations and graphs them!

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Ex: Solve a Linear System of Equations by Graphing (No Solution)

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This video explains how to solve a linear system of equations by graphing. The system is inconsistent. No solutions http://mathispower4u.com

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Explains what no solution is.