At what value of x do the graphs of the equations below intersect
2x-y=6
5x+10y=-10

The graphs of the equations intersect at x=2

Step-by-step explanation:

we have

----> equation A

----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both lines

Using a graphing tool

The solution is the point (2,-2)

see the attached figure

therefore

The graphs of the equations intersect at x=2

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step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4