Question

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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))
ASK FOR HELP​

Answer 1

( -
`(9)/(2)`, -
`(41)/(2)` )

Explanation:

Given the 2 equations

8x = 2y + 5 → (1)

3x = y + 7 → (2)

Rearrange (2) expressing y in terms of x by subtracting 7 from both sides.

y = 3x - 7 → (3)

Substitute y = 3x - 7 into (1)

8x = 2(3x - 7) + 5 ← distribute and simplify right side

8x = 6x - 14 + 5

8x = 6x - 9 ( subtract 6x from both sides )

2x = - 9 ( divide both sides by 2 )

x = -
`(9)/(2)`

Substitute this value into (3) for corresponding value of y

y = 3 × -
`(9)/(2)` - 7 = -
`(27)/(2)` -
`(14)/(2)` = -
`(41)/(2)`

Solution is (-
`(9)/(2)`, -
`(41)/(2)` )