Solve the following system by the substitution method.

Question

need help;

 

Solve the following system by the substitution method.

 

0.1x+0.2y=-0.7

0.2x-0.7y=5.2

Answer 1

Another hmkw problem done for a student who may or may not learn much from this.

Answer 2

0.1x+0.2y=-0.7
0.2x-0.7y=5.2

 

First, multiply each equation by 10 to get rid of the decimal point:

    x + 2y = -7         [eq1]

   2x - 7y = 52       [eq2]

 

To use the substitution method, we need to solve for either x or y.  Let's use [eq1] to solve for x:

    x = -2y - 7          [eq3]

 

Then, we substitute that value for x into the other equation ([eq2]):

    2(-2y-7)  -  7y = 52

 

    -4y - 14  -  7y = 52              [distribute]

       -11y - 14 = 52                     [collect terms]

        -11y = 66                         [add 14 to both sides]

           y = -6                 [divide both sides by (-11)]

 

Now, use either equation to find x [eq3 is modified eq1 and is easy]:

      x = -2y - 7

      x = -2(-6) - 7

      x = 5

 

Check:

  Is    5  + 2(-6) = -7   ?

           5 - 12 = -7   ?

                -7 = -7   ?yes

  Is    2(5) - 7(-6) = 52   ?

          10 + 42 = 52   ?

               52 = 52   ?yes

Answer 3

Substitution method suggests that you would first solve one of these equations for either of those unknowns, x or y. 

0.1x+0.2y=-0.7
0.2x-0.7y=5.2

Let us pick the first one (the choice does not matter though):

0.1x+0.2y=-0.7

Let us solve for x. Subtract 0.2 y first:

0.1x = -0.7 - 0.2y

Divide by 0.1:

x = -7 - 2 y

Now that we found an expression for x, we can substitute this onto the second equation:
0.2x-0.7y=5.2
0.2*(-7-2y) - 0.7y = 5.2
-1.4 - 0.4y - 0.7y = 5.2
-1.4 -1.1y = 5.2
-1.1 y = 5.2 + 1.4
-1.1y = 6.6
y = 6.6/(-1.1)
y = -6

Now that we have y-value, we can get x:
x = -7 - 2y = -7 - 2*(-6) = - 7 + 12 = 5. 

Thus, x = 5, y = -6.