Solve the system by substitution: 2x-y=-6 ; 3y-x=8, Simplify answer?

1...................2x-y=-6
==> y=2x+6 Changing sides and signs

2...................3y-x=8
hence from 1
3(2x+6)-x=8
6x+18-x=8
5x=-10
x=-2

y=2(-2)+6
=2

{x,y}={-2,2}

Solve by using substitution.

2x - y = -6
3y - x = 8

2x - y = -6
y = 2x - (-6)
y = (2x + 6) ...... (1)

3y - x = 8

Substitute (1) for y and solve for x.
3(2x + 6) - x = 8
6x + 18 - x = 8
6x - x = 8 - 18
5x = -10
x = -10/5
x = -2

2x - y = 6

Substitute -2 for x and solve for y.
2(-2) - y = 6
-4 - y = 6
y = -4 - 6
y = -10

∴ x = -2, y = -10

Solve 2x 6 10

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Okay, well I will make your wish comes true and answer them all! Yay! :) 1.) Take the first equation: 3x - 4y = 3 Solve for one of the variables (x or y). I will choose x. Add 4y to both sides so you can solve for x Divide by 3 to both sides to get x by itself Work: 3x - 4y = 3 +4y + 4y -------------------- 3x = 4y + 3 x = 4/3y + 1 Now, plug in your equation for x into the second equation to solve for y. 6(4/3y + 1) + 8y = 54 8y + 6 + 8y = 54 (Distributive Property) 16y + 6 = 54 (Combine like terms) - 6 -6 (Subtract 6 from both sides) ------------------ 16y = 48 y = 3 Now, plug in your numerical value back into the equation you made in the first part to solve for x: x = 4/3 (3) + 1 x = 4 + 1 x = 5 Lastly, you write your x and y values like how you write a coordinate on a graph (x, y) : Answer: (5, 3) Make sense? Let's check our answer: Check: 6 (5) + 8 (3) = 54 30 + 24 = 54 54 = 54 (This is a true statement, since 54 does equal itself. Therefore, you did your algebra right! If you get something like: 47 = 54...well, that's not true, so you must have made an error somewhere. Make sure you check both of your equation with x and y just to be sure. One equation could come out true just by coincidence, but the other one could be wrong) 2.) First equation: 5x + 2y = 9 -5x -5x --------------------- 2y = -5x + 9 y = -5/2x + 9/2 3x - 4 (-5/2x + 9/2) = -31 3x + 10x - 18 = -31 13x - 18 = -31 13x = -13 x = -1 y = -5/2 (-1) + 9/2 y = 5/2 + 9/2 y = 14/2 y = 7 Answer: (-1, 7) 3.) First equation: 2x - 7y = 19 2x = 7y + 19 x = 7/2y + 19/2 -6 (7/2y + 19/2) - 21y = -15 -21y - 57 - 21y = -15 -42y - 57 = -15 +57 +57 ---------------------- -42y = 42 y = -1 x = 7/2 (-1) + 19/2 x = -7/2 + 19/2 x = 12/2 x = 6 Answer: (6, -1) 4.) First Equation: 4x - 11y = -9 4x = 11y - 9 x = 11/4y - 9/4 -6 (11/4 y - 9/4) + 22y = 8 -33/2y + 27/2 + 22y = 8 11/2y + 27/2 = 8 -27/2 -27/2 ---------------------------------- 11/2y = -11/2 y= -1 x = 11/4 (-1) - 9/4 x = -11/4 - 9/4 x = -20/4 x = -5 Answer: (-5, -1) 5.) First Equation: 2x + 2y = 40 2x = -2y + 40 x = -y + 20 (-y + 20) + 4y = 44 3y + 20 = 44 - 20 -20 -------------------- 3y = 24 y = 8 x = -(8) + 20 x = 12 Answer= (12, 8) 6.) Let the variable t stand for the number of true/false questions on the test. Let the variable s stand for the number of short essay questions on the test. Whatever number of variables you have, you must write the same amount of equations for. Since we have two variables, we need to write two equations. Since you know all the true/false and short essay questions will add up to 20 total questions, you can write this equation: t + s = 20 Since we know that each type of questions' point value and the total number of points the questions will add up to on the exam, we can write this equation: 3t + 11s = 100 Now, just like in #'s 1-5, start with your first equation: t + s = 20 s = 20 - t Now, plug in your equation into the second equation: 3t + 11(20 - t) = 100 3t + 220 - 11t = 100 -8t + 220 = 100 - 220 -220 ------------------------- -8t = -120 t = 15 Now, plug your numerical value back into the simplified first equation: 15 + s = 20 -15 -15 ------------------ s = 5 Answer (in a sentence, since it is a word problem): There will be 5 essay questions on the test. Hope this helps! If you want to invest in something, you may want to purchase a fraction calculator, such as the Texas Instruments TI-84 Multiview (that's the one I have). It will help out tremendously when you have those difficult fractions. Smiles, Whitesox27 :D PS. No worries. I checked all the answers already! :) Happy New Year!

6(y+x)=

x = 3y - 8

6y - 16 - y = - 6
5y = 10
y = 2

x = 6 - 8
x = - 2

x = - 2 , y = 2

here's how I would do it

make 2x-y=-6 equal y

add y to both sides 2x=-6+y

add 6 to both side 2x+6=y

now substitute in 2x+6 in for the value of y in 3y-x+8

3(2x+6)-x=8

expand the brackets

6x+18-x=8

5x+18=8

subtract 18 from both sides

5x=-10

divide both side by 5

x=-2

so now we have a value for x we can substitute that into 2x-y=-6

2(-2)-y=-6

-4-y=-6

-4=y-6

-4+6=y

2=y

so the answer is (-2,2)

hope it makes sense!

Solving 2x-y=-6 for y, we get:

2x-y=-6

2x = y - 6

2x + 6 = y

y = 2x +6

Substituting 2x +6 for y in 3y-x=8, we get:

3(2x + 6) - x = 8

Solving for x, we get:

6x + 18 - x = 8

5x +18 = 8

5x = -10

x = -2

Substituting -2 for x in 3y-x=8, we get:

3y - (-2) = 8

3y + 2 = 8

3y = 6

y = 2

So, the solution is (-2, 2).

solve for x in terms of y
3y-x=8
-x=-3y+8
x=3y-8

substitute for x and find y's numerical value
2(3y-8)-y=-6
6y-16-y=-6
5y-16=-6
5y=10
y=2

substitute y for it's numerical value to solve for x
3(2)-x=8
6-x=8
-x=2
x=-2

that's your answer
(-2,2)

2x-y=-6

y = 2x+6

3(2x + 6) - x = 8
6x + 18 - x = 8
5x = -10
x = -2

y = 2(-2) + 6 = 2