Question

System of equations 6x+5y=15 3x+5y=12 (use subtustion)

Answer 1

Answer:

x = 1

y = 9/5

Step-by-step explanation:

Before you can substitute one of the equations into the other, you must isolate one of the variables in one of the equations. For instance, you can rearrange the first equation to isolate the y-variable.

First Equation:                      Second Equation:

6x + 5y = 15                             3x + 5y = 12

6x + 5y = 15                                    <----- First equation

5y = -6x + 15                                   <----- Subtract 6x from both sides

y = (-6/5)x + 3                                 <----- Divide both sides by 5

Now that you have isolated the first equation in terms of "y", you can substitute the equation into the second equation. Then, you can simplify to find "x".

3x + 5y = 12                                    <----- Second equation

3x + 5((-6/5)x + 3) = 12                   <----- Insert first equation into "y"

3x - 6x + 15 = 12                             <----- Multiply terms by 5

-3x + 15 = 12                                   <----- Combine terms with "x"

-3x = -3                                           <----- Subtract 15 from both sides

x = 1                                                <----- Divide both sides by -3

To solve for the y-variable, you can plug x = 1 into either one of the equations. Then, you can simplify to find "y".

6x + 5y = 15                                    <----- First equation

6(1) + 5y = 15                                  <----- Plug 1 in "x"

6 + 5y = 15                                      <----- Multiply 6 and 1

5y = 9                                              <----- Subtract 6 from both sides

y = 9/5                                             <----- Divide both sides by 5