2x + 5y = 7
2x - 3y = 15

1. 2x + 5y = 7

2. 3x + 6y = 3

Multiply Equation 1. by -3 and Equation 2. by 2:

1'.  -6x - 15y = -21

2'.  6x + 12y = 6

Add Equations 1' and 2' to eliminate x

y(-15 + 12) = (-21 + 6)

-3y = -15

y = 5

Substitute this value of y into either Equation 1 or 2 and solve for x:

1. 2x + 5y = 7 ⇒ 2x + 5(5) = 7

2x = (7 - 25) = -18

x = -9

Check

Does 3(-9) + 6(5) = 3?

Does -27 + 30 = 3?

YES!!

Step-by-step explanation:

step-by-step explanation:

compare

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