substitution method

Question

Solve the system of equations by using the substitution method.

 

x+10y=46

3x+6y=18

Answer 1

If you want to solve a system of equations by substitution, you first solve one of the equations for one variable in terms of the other.

 

x+10y=46

subtract 10y from both sides

x=46-10y

 

Now that you know what x equals, you can plug that value into the other equation.

3x+6y=18

3(46-10y)+6y=18

 

Distribute the 3 to get:

138-30y+6y=18

Combine y terms:

138-24y=18

Combine numbers without variables:

-24y=-120

Divide by -24 to solve for y:

y=5

 

Now that you know the value of y. You can go back to either of the original equations and insert its value to solve for x.

For example: x+10(5)=46. Solve for x

Answer 2

Hi Sara, using the substitution method, you solve one of the equations for one of the variables, and then substitute the result into the other equation.

 

Try to pick the simplest equation to solve for one of the variables. In the equations you presented, the first equation is the simplest.

 

Solve for x:

 

x + 10y = 46

 

subtract 10y from both sides:

 

x = 46 - 10y

 

Substitute for x in second equation:

 

3x + 6y = 18

 

3 * (46 - 10y) + 6y = 18

 

138 - 30y + 6y = 18

 

138 - 24y = 18

 

Subtract 18 from both sides:

 

120 - 24y = 0

 

Add 24y to both sides and rearrange:

 

24y = 120

 

Divide both sides by 24:

 

y = 5

 

Substitute for y in the first equation:

 

x + 10y = 46

 

x + 10 * 5 = 46

 

x + 50 = 46

 

Subtract 50 from both sides:

 

x = -4

 

Solution:

 

x = -4

 

y = 5

 

Check:

 

substitute for x and y in the first equation:

 

-4 + 10 * 5 = 46

 

-4 + 50 = 46

 

46 = 46, values check.

 

Questions?