HELP ASAP???

Question

solve this equation using the substitution method.

{-4x-15=5y
{2y=11-5x

Answer 1

Hello Lexi,

 

When using the substitution method, you pick one of the variables (in this case, x or y) to work with first. Which variable you choose is entirely up to you. As you get in more and more algebra practice, you'll get better at picking the variable that will make the problem easier.

 

I'll pick y, and I'll work with the second equation:

 

     2y = 11 - 5x

 

If we divide both sides by 2, we'll end up with:

 

     y = (11 - 5x)/2

 

Distribute the 2 into the parentheses on the right-hand side:

 

     y = (11/2) - (5/2)x

 

Great! Now we can substitute this expression for y in the first equation:

 

     -4x - 15 = 5y

 

     -4x - 15 = 5{ (11/2) - (5/2)x }

 

Distribute the 5 into the parentheses on the right-hand side:

 

     -4x - 15 = (55/2) - (25/2)x

 

Now, collect like terms -- x-terms on the left-hand side, and constant terms on the right-hand side. Add (25/2)x to both sides:

 

     -4x + (25/2)x - 15 = (55/2)

 

Add 15 to both sides:

 

     -4x + (25/2)x = (55/2) + 15

 

Find the lowest common denominator and add:

 

     -(8/2)x + (25/2)x = (55/2) + (30/2)

 

     (17/2)x = (85/2)

 

Multiply both sides by (2/17) to isolate x:

 

     x = (85/2) • (2/17)

 

     x = (85/17)

 

     x = 5

 

Now that you have the value for x, you can go back to any of the two given equations to find the value for y. I'll leave that last bit up to you.

 

It's good practice to make sure that you get the same value for y regardless of which of the two equations you use. If you don't get the same answer for y from both equations, then you need to check your work for errors. It's a quick form of error-checking that will help you score higher on homework assignments, quizzes, and exams.

 

Best of luck! :)

Answer 2

Hi Lexi, to solve a system of equations by substitution, solve one of the two equations for one of the variables. Then substitute that value into the equation.

 

-14x  - 15  = 5y

  

   2y  = 11  - 5x

 

Solve the second equation for y:

 

2y  = 11  - 5x

 

Divide both sides by 2:

 

y = (11 - 5x) / 2

 

Now substitute for y in the first equation:

 

-4x  - 15 = 5 * ((11 - 5x) / 2)

 

Solve this for x.

 

Questions?

Answer 3

This system of equations can be solved by solving either of the two for x or y, and then substituting this result into the other equation. For example, you could solve the second equation for y, and then insert that value of y into the first equation. Solving the second equation for y gives us:

 

y = 1/2 (11 - 5x)

 

Now, you can replace every instance of y in the first equation with 1/2 (11 - 5x) and solve for x. Once you have x, you can then solve for y.