Question

Solve the system of equations using the substitution method:

y - 6x = -15
z - 3x = 2
x + 2y + 3z = 86

Answer 1

To solve the system of equations using the substitution method, first solve for y and z in terms of x, then substitute these expressions into the third equation, solve for x, and finally substitute x back into the expressions for y and z to find their values. The solution is x = 5, y = 15, and z = 17.

Step-by-step explanation:

To solve the system of equations using the substitution method, let's call the first equation (1), the second equation (2), and the third equation (3). First solve equations (1) and (2) for y and z in terms of x:

• y = 6x - 15 (from equation 1)
• z = 3x + 2 (from equation 2)

Now, substitute the expressions for y and z into equation (3):

x + 2(6x - 15) + 3(3x + 2) = 86

Simplify and solve for x:

x + 12x - 30 + 9x + 6 = 86

22x - 24 = 86

22x = 110

x = 5

Now, substitute x back into the equations for y and z to find their values:

• y = 6(5) - 15 = 30 - 15 = 15
• z = 3(5) + 2 = 15 + 2 = 17

So, the solution to the system of equations is x = 5, y = 15, and z = 17.