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Given the system of equations, what is the solution? 5x - 4y = 7 x = 5 - 3/2 y
A. {(61/23, 36/23)}
B. {(-61/23, 36/23)}
c. {(61/23, -36/23)}

Respuesta :

AISstudent
The answer is A


You can solve this by equation the two equations, by substitution method or elimination. Let's choose the substitution since Equation 2 has already X isolated
-take the X in equation 2 and substitute in the first equation
So, You should have 5 (5-3/2 y) -4y =7
Get y ( I'll assume you know how to simplify and find y by yourself )
y=36/23
-Now take y and substitute it in the first equation or the second equation (it doesn't really matter)
Substituting y in Equation 2:
x=5- 3/2 (36/23)
=> x= 61/23

So answer is A where (x,y) is (61/23, 36/23)

Answer:

Option A is correct.

Step-by-step explanation:

Given system of equations are

5x - 4y = 7 ...............(1)

x = 5 - 3/2y .................(2)

value of x from equation (2), put in equation (1)

[tex]5(5-\frac{3}{2}y)-4y=7[/tex]

[tex]25-\frac{15}{2}y-4y=7[/tex]

[tex]-\frac{15}{2}y-\frac{8}{2}y=7-25[/tex]

[tex]\frac{-15-8}{2}y=-18[/tex]

[tex]\frac{-23}{2}y=-18[/tex]

[tex]y=-18\times\frac{-2}{23}[/tex]

[tex]y=\frac{36}{23}[/tex]

Now, Value of x = [tex]5-\frac{3}{2}\times\frac{36}{23}=5-\frac{54}{23}=\frac{115-54}{23}=\frac{61}{23}[/tex]

Solution of given system is [tex](\frac{61}{23},\frac{36}{23})[/tex]

Therefore, Option A is correct.

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