The sum of two numbers is 0. Twice the smaller number subtracted from 3 times the larger number is 10. Let x represent the larger number and y represent the smaller number. Which equations represent this situation?
y=-x
y-ix-5
O
o
y = x
3
y = 2x-5
y-x
2 10
y = 3X+ 3
y=-x
10
y = 3

y = -x and 2y = 3x - 10 is the system of equations.

Step-by-step explanation:

Let,

Larger number = x

Smaller number = y

According to given statement;

x + y = 0

y = -x  

And

3x - 2y = 10

Or it can be written as;

2y = 3x - 10

Therefore,

y = -x and 2y = 3x - 10 is the system of equations.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form