How do you I use the substitution method to solve the following systems: -5x-8y=17 and 2x-7y=-17?

Question

jdoe0001 · Answer

can you solve -> -5x-8y=17 <- for "y"

whpalmer4 · Answer

To use substitution, you solve one of the equations for one of the variables, giving you one variable in terms of the other variable.  Next, you use that substitution equation in the other equation, replacing each use of the variable with the expression you got by solving the first equation for one of the variables.  This gives you an equation in one variable, which you solve.  Then plug the value you got into the substitution equation and find the other variable.

An example:

$$2x+3y = -1$$$$x+2y = -1$$
Here, it is clearly easy to solve the second equation for $x$ in terms of $y$:
$$x+2y=-1$$$$x+2y-2y = -1-2y$$$$x = -1-2y$$Now we take the other equation, and anywhere we find $x$, we replace it with $(-1-2y)$:
$$2x+3y=-1$$$$2(-1-2y)+3y=-1$$$$-2-4y+3y=-1$$$$-2-y=-1$$$$-2=y-1$$$$-1=y$$$$x=-1-2y$$$$x=-1-2(-1)$$$$x=1$$

checking:
$$1+2(-1) = -1$$$$1-2=-1$$$$-1=-1\checkmark$$
$$2(1)+3(-1) = -1$$$$2-3=-1$$$$-1=-1\checkmark$$So our solution passes the test: it works in both equations.  Note that it is possible to come up with a "solution" that only works in one of the equations: the technical term for such a solution is "wrong" :-)  Always test your solutions in all of the equations!