Question

50 points! Solve the following systems of equations.

Answer 1

Let -4x - 15y = 17 be known as equation 1 and -x + y = -13 as equation 2.

To solve the system of equations, we need to determine the value of the "x" and "y" variables. Let us start by determining the value of the y variable.

Note: Since the second equation looks easier to solve for y (in my opinion), I will determine the value of y in the second equation.

This can be done by isolating y on one side of the equation.

Equation 2: $\bold{-x + y = -13}$

Add "x" on both sides of the equation:

$\implies -x + y = -13$

$\implies -x + y + x = -13 + x$

$\implies y = -13 + x$

Therefore, the value of y is -13 + x. Let us substitute the value of y, obtained from equation 2, into equation 1 to determine the value of x.

Equation 1: $\bold{-4x - 15y = 17}$

Substitute the value of y in the equation:

$\implies 4x - 15y = 17$

$\implies -4x - 15(-13 + x) = 17$

Simplify the distributive property:

$\implies -4x - 15(-13 + x) = 17$

$\implies -4x + (195 - 15x) = 17$

$\implies -4x + 195 - 15x = 17$

Combine like terms on both sides:

$\implies -4x + 195 - 15x = 17$                                         

$\implies -19x + 195 = 17$                                                                

Subtract 195 on both sides of the equation:                      

$\implies -19x + 195 = 17$                                                                    

$\implies -19x + 195 - 195 = 17 - 195$                                    

$\implies -19x = -178$                                                                        

Divide -19 on both sides of the equation:                        

$\implies -19x = -178$                                                                

$\implies \dfrac{-19x}{-19} = \dfrac{-178}{-19}$                                                      

$\implies \bold{x = \dfrac{178}{19} }$                                                                        

Now, substitute the value of x in -13 + x to determine the value of y. Once determined, we can put the solution in (x, y) form.

$\implies y = -13 + x$

$\implies y = -13 + \dfrac{178}{19}$          

$\implies y = \dfrac{-247}{19} + \dfrac{178}{19}$ 

$\implies \bold{y = \dfrac{-69}{19} }$

∴ Solution ⇒ (x, y) ⇒ (178/19, -69/19)

Therefore, the solution to the following system of equations is (178/19, -69/19)

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