How do you solve #6x + 5y = -12# and #-9x + y = 69# using substitution?

Question

Nathan Axel · Accepted Answer

#(x,y)=color(blue)(""(-7,6))# Given [1]#color(white)("XXX")6x+5y=-12# [2]#color(white)("XXX")-9x+y=69# re-arranging [1] [3]#color(white)("XXX")y=9x+69# substituting #(9x+69)# from [3] for #y# in [1] [4]#color(white)("XXX")6x+5(9x+69)=-12# simplifying [5]#color(white)("XXX")51x+345=-12# [6]#color(white)("XXX")51x=-357# [7]#color(white)("XXX")x=-7# substituting #(-7)# for #x# in [3] [8]#color(white)("XXX")y=9*(-7)+69=6#

Julia Adams · Answer

undefined To solve the system of equations $6x + 5y = -12$ and $-9x + y = 69$ using substitution, follow these steps:

1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Once you have found the value of one variable, substitute it back into one of the original equations to find the value of the other variable.
5. Check the solution by substituting the values of both variables into both original equations.

Let's start with the given equations:

1. $6x + 5y = -12$
2. $-9x + y = 69$

Let's solve the second equation for $y$:

$-9x + y = 69$

$y = 9x + 69$

Now, substitute $9x + 69$ for $y$ in the first equation:

$6x + 5(9x + 69) = -12$

Now, solve for $x$:

$6x + 45x + 345 = -12$

$51x + 345 = -12$

$51x = -12 - 345$

$51x = -357$

$x = -\frac{357}{51}$

$x = -7$

Now that we have found the value of $x$, let's substitute it back into one of the original equations to find $y$. We'll use the second equation:

$-9(-7) + y = 69$

$63 + y = 69$

$y = 69 - 63$

$y = 6$

So, the solution to the system of equations is $x = -7$ and $y = 6$.

Hazel Anglin · Answer

undefined To solve the system of equations $6x + 5y = -12$ and $-9x + y = 69$ using substitution, follow these steps:

1. Solve one of the equations for one of the variables. We can start with the second equation for ease:
   $$-9x + y = 69$$
   Solve for $y$:
   $$y = 9x + 69$$

2. Substitute the expression for $y$ into the first equation:
   $$6x + 5(9x + 69) = -12$$

3. Distribute and solve for $x$:
   $$6x + 45x + 345 = -12$$
   $$51x = -12 - 345$$
   $$51x = -357$$
   $$x = -7$$

4. Substitute the value of $x$ back into one of the original equations to solve for $y$. Using $y = 9x + 69$:
   $$y = 9(-7) + 69$$
   $$y = -63 + 69$$
   $$y = 6$$

Therefore, the solution to the system of equations is $x = -7$ and $y = 6$.