Solve the following system of equations by the substitution method.

8x = 2y + 5
3x = y + 7

what is the solution set?

{(-41/2, -9/2)}
{(-9/2, -41/2)}
∅

Solution set: {(-9/2, -41/2)}

Step-by-step explanation:

Given that:

8x = 2y + 5   eq1

3x = y + 7 eq2

From eq2 we get:

y =3x -7 eq3

Now putting this value of y in eq1 we get:

8x = 2(3x - 7) + 5

By simplifying we get:

8x = 6x - 14 + 5

8x = 6x -9

8x - 6x = -9

2x = -9

x = -9/2

Putting value of x in eq3

y =3(-9/2) -7

y = -27/2 -7

Taking LCM

y = -27/2 - 14/2

y = -41/2

Hence,

Solution set: {(-9/2, -41/2)}

Now substituting the values of x and y in eq1 and eq2:

8(-9/2) = 2(-41/2) + 5

-72/2 = -41 + 5

-36 = -36

Hence proved

3x = y + 7

3(-9/2) = (-41/2) + 7

-27/2 = -27/2

Hence proved

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