Need with system of equations. let me know if substitution or elimination is used and ! ( also explain how you got the answer in detail. i wanna figure out how to do it on my own).
5x + 4y = -14
3x + 6y = 6

elimination

Step-by-step explanation:

5x + 4y = -14

3x + 6y = 6

S = {-6,4}, x = -6 y = 4

Step-by-step explanation:

the substitution method is when you solve one of the equations for a variable, then plug in that result into the other equation and solve

the addition/elimination method is when you get both equations to have the same value for a variable and 'eliminate' it and solve for the other variable

i personally prefer the substitution method as it allows us to graph easier, but i will demonstrate both methods

SUBSTITUTION METHOD:

to start off, we will solve for one variable in one of the equation. i have chosen to solve for x in 3x + 6y = 6

3x + 6y = 6 < subtract 6y from both sides

3x = -6y + 6 < divide both sides by 3 to isolate x

3x/3 = x

-6y/3 = -2y

6/3 = 2

x = -2y + 2 or x = 2 - 2y

now we will plug in the x value we have found into 5x + 4y = -14

solve: 5x + 4y = -14 when x = 2 - 2y

5(2 - 2y) + 4y = -14 < distribute 5 into 2 - 2y

10 - 10y + 4y = -14 < combine like terms

-10y + 4y = -6y

10 - 6y = -14 < now we solve for y: subtract 10 from both sides

-6y = -24 < divide both sides by -6 to isolate y

-6y/-6 = y

-24/-6 = 4

y = 4

now that we have found y, we can plug this y value in to find x in the system. you can choose any equation you want, i will plug the y value into 3x + 6y = 6

solve: 3x + 6y = 6 when y = 4

3x + 6(4) = 6

3x + 24 = 6 < subtract 24 from both sides

3x = -18 < divide both sides by 3

3x/3 = x

-18/3 = -6

x = -6

our answer to this system of equation is {-6,4}

i will now solve this same system with the addition/elimination method:

ADDITION/ELIMINATION METHOD:

to solve, we need to 'eliminate' one of the variable terms in both equations

5x + 4y = -14

3x + 6y = 6

i will eliminate the x value in this instance, but you can eliminate either variable. to eliminate, we need one negative number and one positive so they cancel out. both 5 & 3 have the number 15 as a common factor, we so we can multiply each number to get 15 in one equation and -15 in another.

-3(5x + 4y = -14)

5(3x + 6y = 6)

we absolutely must multiply the entire equation by the number to get the correct answer. we distribute -3 into 5x + 4y = -14 and 5 into 3x + 6y = 6

-15x - 12y = 42

15x + 30y = 30

add both equations above and -15x & 15x will cancel, thus eliminating the x term

-15x + 15x = 0

-12y + 30y = 18y

42 + 30 = 72

our new equation is:

18y = 72 < divide both sides by 18 to isolate y

18y/18 = y

72/18 = 4

y = 4

now we plug in the y value we have found into one of the equations above. i will plug in y = 4 into 3x + 6y = 6

solve: 3x + 6y = 6 when y = 4

3x + 6(4) = 6

3x + 24 = 6 < subtract 24 from both sides

3x = -18 < divide both sides by 3

3x/3 = x

-18/3 = -6

x = -6

out solution to this system of inequalities is {-6,4}

the solution is the same with both the elimination & substitution method, so you can use any method you want to solve.

please let me know if i need to be more clear!

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