Solve the system of equations: 3x + 2y = 16 and x − y = 1.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to solve the system of equations:

The given system of equations is:

3x + 2y = 16 \quad \text{(1)}

x - y = 1 \quad \text{(2)}

Solve equation (2) for $y$ .
From equation (2), we have:
$x - y = 1$
Add $y$ to both sides:
$x = 1 + y$
Subtract 1 from both sides to isolate $y$ :
$y = x - 1 \quad \text{(3)}$
Substitute the expression for $y$ from equation (3) into equation (1).
Substitute $y = x - 1$ into equation (1):
$3x + 2(x - 1) = 16$
Solve the resulting equation for $x$ .
Distribute the 2:
$3x + 2x - 2 = 16$
Combine like terms:
$5x - 2 = 16$
Add 2 to both sides:
$5x = 16 + 2$ $5x = 18$
Divide by 5:
$x = \frac{18}{5}$ $x = 3.6$
Substitute the value of $x$ back into equation (3) to find $y$ .
Substitute $x = 3.6$ into $y = x - 1$ :
$y = 3.6 - 1$ $y = 2.6$
The solution to the system of equations is:
$x = \boxed{\text{3.6}}$ $y = \boxed{\text{2.6}}$

Answer