Thuy wrote the system of equations
24x+3y = 72
- 18x+y = 30
if the second equation is multiplied by 3. what should the first equation be multiplied by to eliminate the x variable by
addition?

Equation (1) should be multiplied by (9/4) to eliminates the variable x by addition.

Step-by-step explanation:

Here, the given system of equation is:

24 x + 3 y = 72

- 18 x + y  = 30

Now, equation (2) x 3 = - 18(3)  x + (3) y  =(3)  30

⇒  -54 x + 3 y = 90

So, the x term = -54 x

Now, for x to be eliminated in the first term,

24 x should be transformed in to + 54 x as 54 x - 54 x = 0

Let us assume, 24x is multiplied by a factor m so that

24x (m)  = 54 x

⇒  

or, m = 9/4

Hence, equation (1) should be multiplied by (9/4) to eliminates the variable x by addition.

5

step-by-step explanation:

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.