Question

Find all solutions of the given system of equations and check your answer graphically. HINT [First eliminate all fractions and decimals; see Example 3.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).)
x/5 − y/4 = 1
x/6 + y = −4
(x, y) =

Answer 1

Answer:

(x,y)=(0,-4)

Step-by-step explanation:

Given : $\frac{x}{5}- \frac{y}{4} = 1\\\\\frac{x}{6}+ y = -4$

To Find : (x,y)

Solution :

Equation 1 ) $\frac{x}{5}- \frac{y}{4} = 1$

$\frac{4x-5y}{20}= 1$

$4x-5y= 20$  ---A

Equation 2)  $\frac{x}{6}+ y = -4$

$\frac{x+6y}{6} = -4$

$x+6y = -24$  ---B

Solve A  and B by substitution

Substitute the value of x from B in A

$4(-24-6y)-5y= 20$

$-96-24y-5y= 20$

$-96-29y= 20$

$-96-20= 29y$

$-116= 29y$

$\frac{-116}{29}= y$

$-4= y$

Substitute the value of y in B to get value of x

$x+6(-4) = -24$  

$x-24= -24$  

$x=0$  

So,(x,y)=(0,-4)

Check graphically

Plot the lines A and B on graph

$x+6y = -24$ -- Black line

$4x-5y= 20$ -- Purple line

Intersection point gives the solution

So, by graph intersection point is (0,-4)

Hence verified

So, (x,y)=(0,-4)