# What is the value of x and y?How would you solve for y and x(for this triangle) using the quadratic equation: An isosceles triangle's two congruent sides are 2x+3y-5; and 3x+y-1. The two congruent...

How would you solve for y and x(for this triangle) using the quadratic equation: An isosceles triangle's two congruent sides are 2x+3y-5; and 3x+y-1. The two congruent angles of this isosceles triangle are: (3x+2)degrees and (5y-3)degrees.

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According to the rule, an isosceles triangle has 2 sides whose lengths are equal and 2 angles whose measures are also equal.

Form enunciation, the lengths of the equal sides are:

2x + 3y -5 (1)

3x + y -1 (2)

Since they are equal, we'll put (1)=(2):

2x + 3y -5 = 3x + y -1

We'll subtract (2) from (1):

2x + 3y -5 - 3x - y +1 = 0

We'll combine like terms:

x + 2y - 4 = 0 (3)

We'll write the second condition of the given isosceles triangle:

3x +2 = 5y-3

We'll subtract 5y-3 both sides:

3x+2-5y+3 = 0

We'll combine like terms:

3x-5y + 5 = 0 (4)

Now, for finding x and y, we have to solve the system formed by the equations (3) and (4), resulted from the conditions of the isosceles triangle.

x + 2y - 4 = 0

3x-5y + 5 = 0

We'll solve the system using elimination method and we'll eliminate the variable y. For this reason, we'll multiply (3) by 5 and (4) by 2:

5x + 10y - 20 + 6x - 10y + 10 = 0

We'll combine and elimnate like terms:

11x - 10 = 0

We'll add 10 both sides:

11x = 10

x = 10/11

We'll substitute x in (3):

10/11 + 2y - 4 = 0

-34/11 + 2y = 0

2y = 34/11

y = 17/11