Question

find t
?
x - y = 1
x + 3y = 9

Explanation:

Step1: Identify the system of equations

We have the system:

$$\begin{cases} x - y = 1 \\ x + 3y = 9 \end{cases}$$

Step2: Subtract the first equation from the second

Subtract $(x - y)$ from $(x + 3y)$ and $1$ from $9$:
$$(x + 3y) - (x - y) = 9 - 1$$
Simplify left side: $x + 3y - x + y = 4y$
Right side: $8$
So, $4y = 8$

Step3: Solve for y

Divide both sides by 4: $y = \frac{8}{4} = 2$

Step4: Substitute y into the first equation

Substitute $y = 2$ into $x - y = 1$:
$x - 2 = 1$

Step5: Solve for x

Add 2 to both sides: $x = 1 + 2 = 3$

Answer:

$x = 3$, $y = 2$