How do you solve this set of linear equations: 6x−3y=−13;14x−7y=−8?

1 Answer
Shell
Dec 7, 2016

Solve the system.

a6x−3y=−13
14x−7y=a−8

Multiply the first equation by 7 and the second by -3.

a7(a6x−3y=−13)
−3(14x−7y=a−8

a142x−21y=−91
−42x+21y=aa124

Add the two equations.

0x+0y=−67

0=−67aaaFALSE!

There is no solution to this system of equations. In other words, the two lines represented by these equations never intersect and they must be parallel.

Another way to show this is to rearrange the equations in slope-intercept form y=mx+b where #m=slope.

a6x−3y=−13
−6xaaaaa−6x

−3y=−6x−13

−3y−3=−6x−3−13−3

y=2x+133aaaThe slope of the 1st line is 2

14x−7y=a−8
−14xaaaa−14x

−7y=−14x−8

−7y−7=−14x−7−8−7

y=2x+87aaa The slope of the 2nd line is 2.

Both have the same slope of m=2, so the lines must be parallel.

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