Question

solve each system by graphing. tell whether the system has one solution, infinitely many solutions, or no solution. 22. $y = x + 3$; $y = x - 1$ 23. $y = 2x - 1$; $3y = 6x - 5$ 24. $3x + y = 2$; $4y = 12 - 12x$ 25. $2x - 2y = 5$; $y = x - 4$ 26. $y = 2x - 2$; $2y = 4x - 4$ 27. $y - x = 5$; $3y = 3x + 15$ 28. $2x + 2y = 4$; $12 - 3x = 3y$ 29. $2y = x - 2$; $3y = \frac{3}{2}x - 3$ 30. $3x - y = 2$; $4y = -x + 5$ see problem 3. also, looking for an after - school job. one job pays $9 per

Explanation:

Problem 22

Step1: Identify slope/intercept

$y = x + 3$: $m=1$, $b=3$
$y = x - 1$: $m=1$, $b=-1$

Step2: Analyze lines

Parallel (same $m$, different $b$)

Problem 23

Step1: Rewrite second equation

$3y=6x-5 \implies y=2x-\frac{5}{3}$

Step2: Compare slopes/intercepts

$y=2x-1$: $m=2$, $b=-1$
$y=2x-\frac{5}{3}$: $m=2$, $b=-\frac{5}{3}$

Step3: Analyze lines

Parallel (same $m$, different $b$)

Problem 24

Step1: Rewrite equations to slope-intercept

$3x+y=2 \implies y=-3x+2$
$4y=12-12x \implies y=-3x+3$

Step2: Compare slopes/intercepts

Same $m=-3$, different $b=2,3$

Step3: Analyze lines

Parallel lines

Problem 25

Step1: Rewrite first equation

$2x-2y=5 \implies y=x-\frac{5}{2}$

Step2: Compare slopes/intercepts

$y=x-\frac{5}{3}$: $m=1$, $b=-\frac{5}{2}$
$y=x-4$: $m=1$, $b=-4$

Step3: Analyze lines

Parallel (same $m$, different $b$)

Answer:

(22): No solution

---