-6y+7y=4x+2(x-5)-4x+5 3(x+y)-x+y=-10 how to solve the system by the substitution method?

Question

I need help.

Answer 1

Hello Chontra,

 

First step is to simplify the first equation which is -6y+7y=4x+2(x-5)-4x+5.  This is done as follows:

 

 

-1y=4x+2x-10-4x+5

-1y=2x-5 (divide both sides by -1, which changes the sign on everything)

y=-2x+5

 

It also helps greatly to simplify the second part of the equation which is 3(x+y)-x+y=-10 as follows:

3x+3y-x+y=-10

2x+4y=-10

 

Substitute the y=-2x+5 into the second part of the equation as follows:

 

2x+4(-2x+5)=-10

2x-8x+20=-10

-6x+20=-10 (subtract 20 from both sides)

-6x=-30 (divide both sides by -6)

x=5

 

Now that we have solved for x, we can solve for y.  I'll use the simplified second equation to substitute 5 for x as follows:

 

2x+4y=-10

2(5)+4y=-10

10+4y=-10 (subtract 10 from both sides)

4y=-20 (divide both sides by 4)

y=-5

 

Solution set is x=5, y=-5.  Hope this helps!!

Answer 2

Let's simplify the 2 equations first.  The first equation:

-6y + 7y = 4x + 2(x-5) - 4x +5

(-6 + 7)y = 4x + 2x -10 - 4x + 5

y = (4 + 2 - 4)x - 5

y = 2x - 5

 

The second equation:

3(x+y) - x + y = -10

3x + 3y - x + y = -10

(3 - 1)x + (3+1)y = -10

2x + 4y = -10

 

Now substitute the y we got from the 1st equation into the 2nd one:

2x + 4(2x-5) = -10

2x + 8x - 20 = -10

(2 + 8)x - 20 = -10

10x - 20 = -10

10x = 10

x = 1

 

To solve for y, you can substitute your answer, x = 1, into either equation.  I'll use the 1st equation.

y = 2x - 5

y = 2(1) - 5 = -3