Solve the system by using the substitution method?

Question

the problem:
X -7Y=16
-3X+6Y= -3

Please can someone explain how to figure this problem.. Thanks so very much

Answer 1

The substitution method, an alternative method to the elimination method, involves solving one equation in terms of one variable, and plugging it into the other. We have

x - 7y = 16
-3x + 6y = -3

Let's take the first equation, and solve for x. Bring 7y to the right hand side, to get

x = 7y + 16

NOW, plug this value for x, into the second equation, -3x+6y=-3

-3(7y+16) + 6y = -3
-21y - 48 + 6y = -3
-15y = 45
y = -3

Now that we have y = -3, we can solve for the other variable x by plugging y = -3 into any one of the two given equations. I'll leave that up to you.

Answer 2

I am numbering the 2 equations to make this clearer:
1.) x-7y=16
2.)-3x+6y=-3

1.) x=7y+16 is the same as x-7y=16
Put that in for x in equation #2:(7y+16)
-3(7y+16) +6y=-3
Solve for that equation
-21y-48+6y= -3
-15y-48= -3
-15y=45
y= -3

Then put the -3 into the other equation:
x-7(-3)=16
x+21=16
x= -5

ANSWERS: y= -3; x= -5

Answer 3

first. let's see the first equation:
x - 7y = 16
we can write this way: x = 16 + 7y

now, look at the 2nd equation

-3x + 6y = -3

remember, we know from the first equation that x = 16 + 7y

so, -3 (16 + 7y) + 6y = -3
-48 - 21y + 6y = -3
15y = -45
y = -3

x = 16 + 7y
x = 16 + 7 (-3)
x = -5

Answer 4

Given eqns are multiplied by a common factor in such a way that, either x term or y term is cancelled upon either addition or subtraction..

eg: [ x - 7y = 16 ] ...(i)
[ -3x + 6y = -3 ] ...(ii)
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[ x - 7y = 16 ] * 3
[ -3x + 6y = -3 ]

Note: I m multiplying the 1st eqn by 3 as the x-term gets cancelled upon addition.. similarly, the 1st eqn can be multiplied by 6 n the 2nd eqn by 7 so that y term get cancelled out upon addition of the eqns...

so, now, the eqns are:
3x - 21y = 48
-3x + 6y = -3

solving those eqns (adding these eqns), we get,
-15y = 45
=> y = -3

sub this value of y in eqn (ii), we get,
-3x+6(-3)=-3
=> -3x-18=-3
=> -3x = 15
=> x= -5

Hence, the values of x and y are:

x = -5 and y = -3.

Answer 5

X = 7Y + 16

-3(7Y+16) + 6Y = -3
-21Y - 48 + 6Y = -3
-15Y = -3 + 48

Y= 45/-15

Y= -3

SUBSTITUTE Y VALUE IN THE FIRST EQUATION

X-7(-3) = 16
X+21 = 16

X = 16 - 21

X = - 5

Answer 6

Substitution method is when you solve for one variable in terms of another variable and then plug that value into the corresponding variable in the other equation:

x = 16 + 7y

Plug it into the other equation and solve for y. Then after solving for y, solve for x.