Question

What is the answer using either the substitution method or elimination method

Answer 1

To solve this problem, I am going to use the substitution method.  To do this, we use our first equation given (s=4r-1) and substitute this given value for s (4r-1) and substitute it into the second equation so that we have an equation with only one variable.  This is modeled below:

s = 4r - 1

6r - 5s = -23

6r - 5(4r-1) = -23

Now, we can solve this equation as we would any other equation, using the order of operations outlined by PEMDAS.  To begin, we will distribute the factor of -5 through the parentheses on the left side of the equation.

6r - 20r + 5 = -23

Next, we should combine like terms on the left side of the equation:

-14r + 5 = -23

Next, we should subtract 5 from both sides of the equation to get the variable term alone on the the left side of the equation.  We get:

-14r = -28

Finally, we should divide both sides by -14 to get the variable r alone on the left side of the equation.

r = 2

Now that we know that value for the variable r, we can substitute this value into one of our original equations (either one will work, but I am choosing to use the first one):

s = 4r - 1

s = 4(2) - 1

Now, we can find the value for s by using multiplication and then subtraction to simplify the right side of the equation.

s = 8-1

s = 7

Therefore, your answer is s = 7 and r = 2.

Hope this helps!