Final answer:
To solve the provided system of linear equations, isolate one variable, substitute into the other equation, solve for the first variable, and then use the solution to find the second variable. The solution is (x = 3, y = -4).
Step-by-step explanation:
To solve the system of equations:
- x - 3y - 15 = 0
- -4x - y = -8
Step 1: Identify the knowns. We have two equations:
- Equation 1: x - 3y - 15 = 0
- Equation 2: -4x - y = -8
Step 2: Choose an equation to begin with. Let's use Equation 2.
Step 3: Isolate one variable. For example, we can solve Equation 2 for y:
-4x - y = -8
y = -4x + 8
Step 4: Now, substitute y in Equation 1 with the expression found in Step 3:
x - 3(-4x + 8) - 15 = 0
Step 5: Solve for x after substitution:
x + 12x - 24 - 15 = 0
13x - 39 = 0
x = 3
Step 6: Substitute x into any one of the original equations. Let's use Equation 2:
-4(3) - y = -8
y = -4(3) + 8
y = -12 + 8
y = -4
Step 7: Check the solution (x=3, y=-4) in both original equations to ensure it works.
The answer to the student's question is the solution set (x = 3, y = -4).