Question

Find three solutions to the system of equations.

37. {x+2y+z=5; y+3z=9}
38. {x+5y+3z=9; 2x+9y+7z=5}

Answer 1

Three solutions to the system of equations are:

x = -8, y = 5, z = 1

x = 0, y = 3, z = 2

x = -5, y = 7, z = 0

Step-by-step explanation:

Solve for y in the first equation of each system:

Equation 37: y = (5 - x - z) / 2

Equation 38: y = (9 - x - 3z) / 5

Substitute these expressions for y in the second equation of each system:

Equation 37: x + 2((5 - x - z) / 2) + z = 5

Equation 38: x + 5((9 - x - 3z) / 5) + 3z = 9

Solve the resulting equations for x and z:

Equation 37: x = -8, z = 1 (leads to y = 5)

Equation 38: x = 0, z = 2 (leads to y = 3)

Equation 38 also has a second solution with x = -5, z = 0 (leads to y = 7)

Therefore, the system has three solutions: (-8, 5, 1), (0, 3, 2), and (-5, 7, 0).