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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) =

Respuesta :

Answer:

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

Step-by-step explanation:

Given : [tex]\frac{x}{5}- \frac{y}{4} = 1\\\\\frac{x}{6}+ y = -4[/tex]

To Find : (x,y)

Solution :

Equation 1 ) [tex]\frac{x}{5}- \frac{y}{4} = 1[/tex]

[tex]\frac{4x-5y}{20}= 1[/tex]

[tex]4x-5y= 20[/tex]  ---A

Equation 2)  [tex]\frac{x}{6}+ y = -4[/tex]

[tex]\frac{x+6y}{6} = -4[/tex]

[tex]x+6y = -24[/tex]  ---B

Solve A  and B by substitution

Substitute the value of x from B in A

[tex]4(-24-6y)-5y= 20[/tex]

[tex]-96-24y-5y= 20[/tex]

[tex]-96-29y= 20[/tex]

[tex]-96-20= 29y[/tex]

[tex]-116= 29y[/tex]

[tex]\frac{-116}{29}= y[/tex]

[tex]-4= y[/tex]

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

[tex]x+6(-4) = -24[/tex]  

[tex]x-24= -24[/tex]  

[tex]x=0[/tex]  

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

Check graphically

Plot the lines A and B on graph

[tex]x+6y = -24[/tex] -- Black line

[tex]4x-5y= 20[/tex] -- Purple line

Intersection point gives the solution

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

Hence verified

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

Ver imagen wifilethbridge

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