tell which equation you would choose to solve for one of the variables when solving the system by substitution. explain.

Question

y=5x-2

2x+9y=10    

 

 

3x-7y=12

3x-12y=6 

 

 

1/5x+y=8

4x-3y=1

Answer 1

I'm guessing that you're looking for the answer for each of the three systems...

 

The idea of substitution is that if one variable lets you express one variable in terms of the other, you can substitute that expression for the variable in the other equation.  That way the second equation only has one variable, and you can solve that.

 

y=5x-2
2x+9y=10

 

The first equation says that y is 5x-2.  So you can put "5x-2" in place of y in the second equation...

 

2x+9(5x-2)=10

 

... and solve for x.

 

 

3x-7y=12
3x-12y=6

 

The coefficients of the second equation are all multiples of 3.  If you divide both sides of that equation by 3, you get:

 

x - 4y = 2

 

Now add 4y to both sides and you get:

 

x = 4y + 2

 

So now you have an expression for x in terms of y, and you can use that in the other equation:

 

3x-7y=12

3(4y + 2) - 7y = 12

 

...and solve for y

 

 

1/5x+y=8
4x-3y=1

 

Multiply both sides of the first equation by 5 and you get:

 

x + 5y = 40

 

Subtract 5y from both sides and you get:

 

x = -5y + 40

 

So it's the same as the other cases.  You can substitute -5y + 40 for x in the second equation and solve it for y.

 

4x-3y=1

4(-5y + 40) -3y = 1