How do you solve the system of equations 7x=2y+1 and 4y=-3x+15 by using substitution?

7x = 2y + 1    ...(1)

4y = -3x + 15  ...(2)

 

Divide each term in (2) by 4

y = -(3/4)x + 15/4    ...(3)

 

Replace the y in (1) using (3)

7x = 2[-(3/4)x + 15/4]

7x = -(3/2)x + 15/2

 

Multiply each term on both sides by 2

14x = -3x + 15

 

Add 3x to both sides

17x = 15

 

Divide both sides by 17

x = 15/17

 

Substitute this back into (3)

y = -(3/4)*(15/17) + 15/4

y = (15/4)*(-3/17 +1)

y = (15/4)*14/17

y = 15*7/(2*17)

y = 105/34

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