Question

Math help! will reward medal!

The system of equations is coincident.

What are the missing values?
-2x+5y=-12
-6x+____ y=_____

Answer 1

@K12girlohva please help!

Answer 2

please multiply both sides of first equation by \(3\)

Answer 3

what do you mean? @Michele_Laino

Answer 4

hint:
\[\huge\left( { - 2x + 5y} \right) \cdot 3 = \left( { - 12} \right) \cdot 3\]
please simplify

Answer 5

I still don't quite understand how to do that exactly...... @Michele_Laino

Answer 6

next step:
if I apply the distributive property of multiplication ove addition, I get:
\[\huge \left( { - 2} \right) \cdot 3x + 5 \cdot 3y = - 36\]
please continue

Answer 7

what is \((-2) \cdot 3=...?\)

Answer 8

what is \(5 \cdot 3=...?\)

Answer 9

the first one: -6
the second one: 15

Answer 10

@Michele_Laino

Answer 11

so we can write this:

\(\huge -6x+15y=-36\)

so, what are the missing coefficients

Answer 12

please compare such equation with the incomplete second equation which you provided

Answer 13

x and y @Michele_Laino

Answer 14

If the system is coincident, that means the two equations are the same line.
That means that one equation is simply a multiple of the other equation.
\(−2x+5y=−12\)
\(−6x+\_\_\_\_y=\_\_\_\_\)

If the second equation is a multiple of the first equation, there is a number that you multiply the first equation by to get the second equation.
The only corresponding coefficients that you see in both equations are the coefficients of x: -2 and -6.
What do you multiply -2 by to get -6?
That's what you need to multiply the other coefficients of the first equation to get the second equation.

Answer 15

3 @mathstudent55

Answer 16

do you get the idea? the 2nd equation has a missing 15 (in front of the y) and -36 on the right side of the = sign.

Answer 17

Correct.
Now that you know the number is 3, multiply the other coefficients of the first equation by 3 to get the second equation.

\(−2x+5y=-12\)

\(3 \times (−2x)+ 3 \times 5 y=3 \times (-12)\)

\(-6x + 15y - 36\)