Solve each system of equations by graphing.

50.

x2y=102x4y=12

Short Answer

Expert verified

There is no solution of the given system of equations.

Step by step solution

01

­- Description of step.

Number the given system of equations.

x2y=1012x4y=122

02

­- Description of step.

The first equation is: x-2y=10.

When x=0,

02y=102y=10y=5

Therefore, when x=0, y=-5.

When x=2,

22y=102y=8y=4

Therefore, when x=2, y=-4

Therefore, the equation x-2y=10 is the equation of the line passing through the points 0,-5 and 2,-4.

03

­- Graph the equation x-2y=10.

The graph of the equation x-2y=10 is:

04

­- Description of step.

The second equation is: 2x-4y=12.

When x=0,

2x4y=12204y=1204y=124y=12y=3

Therefore, when x=0, y=-3.

When x=2,

224y=1244y=124y=8y=2

Therefore, when x=2, y=-2

Therefore, the equation 2x-4y=12 is the equation of the line passing through the points 0,-3 and 2,-2.

05

­- Graph the equation 2x-4y=12.

The graph of the equation 2x-4y=12 is:

06

­- Graph the equations x-2y=10 and 2x-4y=12.

The graph of the equations x-2y=10 and 2x-4y=12 is:

07

­- Description of step.

From the graph of the equations x-2y=10 and 2x-4y=12, it can be noticed that the lines are parallel to each other and therefore there is no point of intersection of these lines.

The solution of the system of linear equations in two variables is given by the intersection point of the lines.

Therefore, there is no solution of the given system of equations.

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