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The equations were multiplied by constants and added together to determine that the value of x in the system of equations is –4. Negative three-fourths x minus two-thirds y = negative 1 One-half x minus five-sixths y = negative 7 What is the value of y? a. –6 b. –3 c. 3 d. 6

Respuesta :

calculista

Answer:

Option d. 6

Step-by-step explanation:

we have

[tex]-\frac{3}{4}x-\frac{2}{3}y=-1[/tex] ----> equation A

[tex]\frac{1}{2}x-\frac{5}{6}y=-7[/tex] -----> equation B

Multiply the equation A by -5/4 both sides

[tex](-\frac{5}{4})(-\frac{3}{4}x)+(-\frac{5}{4})(-\frac{2}{3}y)=-1(-\frac{5}{4})[/tex]

[tex](\frac{15}{16})x+(\frac{10}{12}y)=\frac{5}{4}[/tex]

[tex]\frac{15}{16}x+\frac{5}{6}y=\frac{5}{4}[/tex] -----> equation C

Adds equation B and equation C

[tex]\frac{1}{2}x-\frac{5}{6}y=-7\\\\\frac{15}{16}x+\frac{5}{6}y=\frac{5}{4}\\\\-------------\\\\\frac{1}{2}x+\frac{15}{16}x=-7+\frac{5}{4}\\\\\frac{23}{16}x=-\frac{23}{4}\\\\x=-4[/tex]

Find the value of y

substitute the value of x in equation A

[tex]-\frac{3}{4}(-4)-\frac{2}{3}y=-1[/tex]

[tex]\frac{2}{3}y=4\\\\y=6[/tex]

Answer:

D. 6

Step-by-step explanation:

it is right