$1.\\\left\{\begin{array}{ccc}y=3x&(1)\\2y=6x&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(3x)=6x\\6x=6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\6x-6x=6x-6x\\0=0\qquad\text{TRUE}\\\\Answer:\ \text{Infinitely many solutions}\\\\\left\{\begin{array}{ccc}y=3x\\x\in\mathbb{R}\end{array}\right$

$2.\\\left\{\begin{array}{ccc}y=2x+5&(1)\\y-2x=1&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\(2x+5)-2x=1\\2x+5-2x=1\qquad\text{combine like terms}\\(2x-2x)+5=1\\5=-1\qquad\text{FALSE}\\\\Answer:\ \text{No solution.}$

$3.\\\left\{\begin{array}{ccc}3x-2y=9\\-6x+4y=1&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x-2y=9\\-3x+2y=0.5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=9.5\qquad\text{FALSE}\\\\Answer:\ \text{No solution.}$

5 0

3 years ago

Tell whether -2 is a solution of the inequality n-5<8

ruslelena [56]

Answer:

-2 is a solution

Step-by-step explanation:

-2-5<8

-7<8

6 0

3 years ago

a line that includes the point (3,4) has a slope of 2. what is the equation in the slope-intercept form?

Andreas93 [3]

Answer:

y=2x-2

Step-by-step explanation:

the slope is y/x

the slope is 2 or 2/1

subtract 2 from the y value and 1 from the x value

(3-1,4-2) = (2,2)

keep doing this until you get a 0 in the x value

(2-1,2-2) = (1,0)

1 is your x-intercept

(1-1,0-2) = (0,-2)

-2 is your y intercept.

So now you know your y-intercept and your slope so you can now write your equation.

y=mx+b

m=slope, b=y-intercept

m=2, b=-2

substitute into the equation

y=2x-2

8 0

3 years ago