Question

Use the given information to write and solve a system of linear equations to find the values of x and y.

Answer 1

x=5, y=2 | Equations: 4x+y=22 (or see below) and 12x-5y=50

Explanation:

Here's my attempt:

First Equation:

Because triangles ΔSTU and ΔXYZ are congruent, then we can say that:
m∠S = m∠X
m∠T = m∠Y
m∠U = m∠Z

We know that m∠X = 130°, and that m∠X = m∠S, so m∠S = 130°

We also know that the sum of angles in a triangle = 180°

We also know the rest of the angles in ΔSTU: 28° and (4x+y)°

So, we can say that ∠S + ∠T + ∠U = 130+28+4x+y = 180 (we can remove the degree sign)

Now, you can either enter this as it is or simplify it: ❗

130+28+4x+y=180

4x+y+158=180

4x+y=22

Second Equation:

We can do the same thing as for the first equation and get the angles of ΔXYZ:

∠X = 130, ∠Y = 8x-6y, ∠Z = 4x+y

Then, add them and set it to 180:

130+8x-6y+4x+y=180

Simplify:

12x-5y+130=180

12x-5y=50

To solve for x and y:

Now, we have to solve the systems.

Let's start with the first one:

4x+y=22

Isolate y:

y=22-4x (Equation 1)

Then, we plug it into the second equation:

12x-5y=50

12x-5(22-4x)=50

12x-110+20x=50

32x=160

x=5

So we got x, but to find y, we need to plug in x into Equation 1 (where we isolated y

y=22-4x

y=22-4(5)

y=22-20

y=2

We have both our x and y values

That was my attempt, hope it helped!

Answer 2

The values of x and y are 5 and 2, respectively.

Because triangles ΔSTU and ΔXYZ are congruent, then we can say that:

m∠S = m∠X

m∠T = m∠Y

m∠U = m∠Z

We already know that mX = 130° and that mX = mS, hence mS = 130°.

We also know that the sum of a triangle's angles equals 180°.

We also know the remaining angles in STU: 28° and (4x+y)°

As a result, S + T + U = 130+28+4x+y = 180. (The degree symbol can be removed)

You can now either enter this as is or simplify it:

130+28+4x+y=180 4x+y+158=180

4x+y=22

The second equation is as follows:

We may use the same method as in the previous equation to find the angles of XYZ:

X = 130, Y = 8x-6y, and Z = 4x+y.

Then combine them and set it to 180:

130+8x-6y+4x+y=180

To simplify, 12x-5y+130=180.

12x-5y=50

To find x and y, do the following:

Now we must deal with the systems.

Let's begin with the first:

4x+y=22

Identify y: y=22-4x (Equation 1)

We then enter it into the second equation:

12x-5y=50

12x-5(22-4x)=50

12x-110+20x=50 32x=160

x=5

So we got x, but to find y, we need to plug in x into Equation 1 (where we isolated y

y=22-4x

y=22-4(5)

y=22-20

y=2

Therefore the values of x and y are 5 and 2, respectively.