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MATHEMATICAL CONNECTIONS Use the given information to write and solve a system of linear equations to find the values of $x$x​ and y$y$y​ . The text reads triangle L M N is congruent to triangle P Q R, the measure of angle L equals 40 degrees, the measure of angle M equals 90 degrees, the measure of angle P equals left parenthesis 17 x minus y right parenthesis degrees, the measure of angle R equals left parenthesis 2 x plus 4 y right parenthesis degrees. The equations are is equal to 40$=\ 40$= 40​ and is equal to 50$=\ 50$= 50​ . Question 2 $x\ =$x =​ and $y\ =$y =​

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abidemiokin

The value of x and y is 2 and 11.5

The sum of the interior angle of a triangle is 180 degrees.

Since LMN and PQR are similar, hence:

m<L = m<P

m<M = m<Q

m<N = m<R

Given the following parameters

m< L = 40 degrees

m<M = 90 degrees

m<P = 17x - y

m<R = 2x + 4y

Get the measure of m<N

m<M + m<N + m<L = 180

90n+ m<N + 40 = 180

m<N = 180 - 130

m<N = 50degrees

Since m<P = m<L, hence;

17x - y = 40 ....... 1

Also m<R = m<N

2x + 4y = 50 .......... 2

Solve simultaneously

17x - y = 40 ....... 1  * 4

2x + 4y = 50 .......... 2 * 1

___________________________

68x - 4y = 160

2x + 4y = 50

Adding both equations

68x + 2x = 160 + 50

70x = 210

x = 2

Substitute x = 3 into the equation 2x + 4y = 50

2(2) + 4y = 50

4 + 4y = 50

4y = 50 - 4

4y = 46

y = 46/4

y =  11.5

Hence the value of x and y is 2 and 11.5

Learn more here: https://brainly.com/question/15165519

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