If 2x+6y=2 and -7+5y=x, what is 2x?

3 Answers
Jan 24, 2018

2x=-4

Explanation:

You can solve this by using a system of equations and the substitution method.

2x+6y=2
-7+5y=x

Since the second equation has an x=, substitute it for the x in the first equation.

2(-7+5y)+6y=2

Solve for y like you would any other equation.

-14+10y+6y=2
16y=16
y=1

Finally, plug your new y value into either of the original equations and solve. Here, I used the second one.

-7+5(1)=x
x=-2

Multiply this x value by 2 to find 2x.

2x=2(-2)=-4

Hope this helps!

Jan 24, 2018

2x=-4

Explanation:

2x+6y=2to(1)

-7+5y=xto(2)

"substitute "x=-7+5y" into equation "(1)

2(-7+5y)+6y=2

rArr-14+10y+6y=2

rArr-14+16y=2

"add 14 to both sides"

cancel(-14)cancel(+14)+16y=2+14

rArr16y=16

"divide both sides by 16"

(cancel(16) y)/cancel(16)=16/16

rArry=1

"substitute "y=1" into equation "(2)

-7+5=xrArrx=-2

rArr2x=2xx-2=-4

Jan 24, 2018

color(blue)(2x = (-4)

Explanation:

Given:

color(blue)(2x+6y=2) color(red)(Equation.1)

color(blue)(-7+5y=x) color(red)(Equation.2)

color(green)(Step-1)

We can write color(red)(Equation.2) as

-7+5y=x

Add color(green)(+7 on both side of the equation:

-7+5y color(green)(+7=x color(green)(+7

-cancel 7+5y color(green)(+ cancel 7=x color(green)(+7

5y =x +7

Add color(brown)((-x) on both side of the equation:

5y+ color(brown)(-x) =x +7+color(brown)(-x)

5y+ color(brown)(-x) =cancel x +7+color(brown)(- cancel x)

5y -x =7

color(blue)(-x + 5y =7 color(red)(Equation.3)

color(green)(Step-2)

Consider:

color(blue)(2x+6y=2) color(red)(Equation.1)

color(blue)(-x + 5y =7 color(red)(Equation.3)

Multiply each term in color(red)(Equation.3) by 2 to get

color(blue)(-2x + 10y =14 color(red)(Equation.4)

Add color(red)(Equation.1) and color(red)(Equation.4)

color(blue)(2x+6y=2) color(red)(Equation.1)

color(blue)(-2x + 10y =14 color(red)(Equation.4) to get

16y=16

Divide each term by 16

(16y)/16=16/16

(cancel 16*y)/ cancel 16=16/16

Hence,

color(blue)(y= 1

color(green)(Step-3)

Substitute color(blue)(y= 1 in

color(blue)(2x+6y=2) color(red)(Equation.1)

2x+6*1 =2

2x+6 =2

Add (-6) to both sides

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

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

2x=-4

Divide both sides by 2

(2x)/2=(-4)/2

(cancel 2x)/cancel 2=(-4)/2

color(blue)(x=(-2)

So, we have

color(blue)(x=(-2)

color(blue)(y= 1

You want to find the value of color(brown)(2x

color(blue)(2x = 2*(-2) = -4)

Hence

color(blue)(2x = (-4)

Hope this helps.