Question

1. $\

$$\begin{cases} y = x + 8 \\\\ x + y = 2 \\end{cases}$$

$

1. $\

$$\begin{cases} y = x + 2 \\\\ 3x + 3y = 6 \\end{cases}$$

$

1. $\

$$\begin{cases} y = 2x + 1 \\\\ 2x - y = 3 \\end{cases}$$

$

Explanation:

Problem 3

Step1: Substitute $y=x+8$ into second equation

$x + (x + 8) = 2$

Step2: Simplify to solve for $x$

$2x + 8 = 2 \implies 2x = 2 - 8 \implies 2x = -6 \implies x = -3$

Step3: Substitute $x=-3$ into $y=x+8$

$y = -3 + 8 = 5$

Problem 5

Step1: Substitute $y=x+2$ into second equation

$3x + 3(x + 2) = 6$

Step2: Simplify and solve for $x$

$3x + 3x + 6 = 6 \implies 6x = 6 - 6 \implies 6x = 0 \implies x = 0$

Step3: Substitute $x=0$ into $y=x+2$

$y = 0 + 2 = 2$

Problem 7

Step1: Substitute $y=2x+1$ into second equation

$2x - (2x + 1) = 3$

Step2: Simplify and check consistency

$2x - 2x - 1 = 3 \implies -1 = 3$

Answer:

1. For problem 3: $x=-3$, $y=5$
2. For problem 5: $x=0$, $y=2$
3. For problem 7: No solution (contradiction, $-1

eq 3$)