To solve for x and y, set up two equations based on congruent angles in the triangles. Solve the system using substitution or elimination to get x = 25.25 and y = 29.
To solve the system of linear equations for the congruent triangles △STU and △XYZ, we need to set up two equations based on the information given. First, since the triangles are congruent, their corresponding angles are equal. This means that m∠U, which is given as (4x + y)°, must be equal to m∠X, which is 130°. The equation we can write from this is:
4x + y = 130 ... (1)
Similarly, m∠T in △STU is 28°, and because m∠T corresponds to m∠Z in △XYZ, and m∠Z is equal to m∠Y (since angles Z and Y are both opposite equal sides in the congruent triangles), the equation formed from the angles at Y and T is:
8x - 6y = 28 ... (2)
Now we have a system of equations to solve for x and y:
To solve this system, we can use the method of substitution or elimination. For simplicity, we can multiply equation (1) by 6 to eliminate y:
6(4x + y) = 6(130)
24x + 6y = 780 ... (3)
Now, by adding equation (2) and equation (3), we get:
24x + 6y + 8x - 6y = 780 + 28
32x = 808
x = 25.25
Substituting x back into equation (1) to solve for y, we get:
4(25.25) + y = 130
101 + y = 130
y = 29
Thus, the solution to the system of equations is x = 25.25 and y = 29.