Find the solution to the systems of equations using the elimination method. 2x + 3y = 11
5x + 3y = 14

x = 1 ; y = 3

Step-by-step explanation:

5(2x + 3y = 11)

2(5x + 3y + 14)

(distribute)

10x + 15y = 55

10x + 6y = 28

(subtract)

9y = 27

(divided 9 to both sides)

9 divided by 9 cancels out and 27 divided by 9 = 3

so..

y = 3

now, using any equation, (i’ll be using 2x + 3y =11) plug in the y value to find the x value

2x + 3y = 11

2x + 3(3) = 11

(multiply 3 x 3)

2x + 9 = 11

(subtract 9 from 9 and 11)

2x = 2

(divide 2 from both sides)

2 divided by 2 = 1

therefore...

x = 1

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

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step-by-step explanation: