solve using the substitution method. y-2x=-6 2y-x=5?

Answer 1

first you solve one of the equations for y...

then you substitute that value into the other equation for every y...

y - 2x = -6
y = 2x - 6 (added 2x to both sides) now substitute this into the other equation...

2y - x = 5
2(2x - 6) - x = 5 (substituted 2x - 6 for y)
4x - 12 - x = 5 (distributed the 2 through inside the parenthesis)
4x - x - 12 = 5 (re-arranged by commutative law)
3x - 12 = 5 (subtracted x from 4x)
3x - 12 + 12 = 5 + 12 (add 12 to both sides)
3x = 17 (simplified)
x = 17/3 (divided both sides by 3)

NOW.. put this value of x into one of the equations and solve it for y...
y - 2(17/3) = - 6
y - 34/3 = - 6
y = -6 + 34/3 (added 34/3 to both sides)
y = -6 + 11+1/3 (34/3 is 11 and 1/3)
y = 5+ 1/3 (subtracted 6 from 11)
y = 15/3 + 1/3
y = 16/3

(17/3, 16/3) is the point where your equations are equal.. (x,y) coordinates.

Answer 2

Hi, you can eliminate either using x or y. Lets take x.

From 2y - x = 5 follows x = 2y - 5.

In the first equation we introduce this exression for x

y - 2*(2y - 5) = -6

Multiplying the second term on the left side

y - 4y + 10 = -6

-3y + 16 = 0 y = 16/3

x = 2y - 5 = 32/3 - 15/3 = 17/3

At the end you should always check the solution.

y - 2x = -6 16/3 -2*17/3 =- 18/3 is a true statement
2y - x = 5 32/3 - 17/3 = 5 is a true statement

Answer 3

In case you need to show the work....

Y - 2X= -6, therefore, Y must = -6 + 2X. Substitute this into the other equation and you get: 2 (-6 + 2X) - X = 5. Distribute the 2 and you'll get: -12 + 4X - X = 5. Do the rest of the math and you get: -12 + 3X = 5. Add like terms. 3X = 17. Divide both sides by 3 to get: x = 17/3.

Answer 4

*SOlve for "x" or, "y" in either equation. Let's solve for "y" in the 1st equation..

First: add "2x" to both sides...

y - 2x + 2x = - 6 + 2x
y = - 6 +2x

Sec: replace "-6+2x" with the y-variable in the 2nd equation...

2(-6+2x) - x = 5

*Eliminate parenthesis - multiply the outer term with the terms in the parenthesis...

2(-6) + 2(2x) - x = 5
- 12 + 4x - x = 5
- 12 + 3x = 5

*Add "12" to both sides...

-12 + 12 + 3x = 5 + 12
3x = 17

*Isolate "x" by divide both terms by 3...

3x/3 = 17/3
x = 17/3

Third: replace "17/3" with the x-variable in the 1st equation...

y - 2(17/3) = - 6
y - (2*17)/3 = - 6
y - 34/3 = - 6

*Add "34/3" to both sides...

y - 34/3 + 34/3 = - 6 + 34/3
y = 16/3

Solution: (17/3,16/3)

Answer 5

x=17/3

Answer 6

y-2x=-6
2y-x=5

y= 2x-6

2(2x-6)-x=5
4x-12-x=5
3x-12=5
3x= 17
x= 17/3

2y-17/3=5
2y= 32/3
y=16/3

ans: (17/3,16/3)

Answer 7

Easy one i think!

y=2x+6 then fill that in
2(2x+5)-x=5
4x+10-x=5
3x=5
x=5/3 or 1.6

Answer 8

y=2x-6
2(2x-6)-x=5
4x-12-x=5
3x-12=5
3x=17
x=17/3
y=2(17/3)-6
y=34/3-6
y=34/3-18/3
y=16/3