Question

How do you solve by substitution: 3x-8y=-7 and -5x-6y=3?

Answer 1

`y = -34/38 and x = -269/57`

Explanation:

`x = (-7 + 8y)/3`

-5(x) - 6y = 3
-5((-7 + 8y)/3) - 6y = 3

(35)/3 + (40y)/3 - 6y = 3
35 + 40y -2y = 1
38y = -34
y = -34/38

x = (-7 + 8(-34/38))/3
x = -269/57

Answer 2

`y=+13/29`

I will let you finish off

Explanation:

Given:
`+3x-8y=-7" ".........................Equation(1)`
`-5x-6y=3" ".............................Equation(2)`

Consider `Eqn(1)`

Add `8y` to both sides

`3x=8y-7`

Divide both sides by 3

`color(red)(x=8/3y-7/3)" "...........................Equation(1_a)`
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Using `Eqn(1_a)` substitute for `x` in `Eqn(2)`

`color(green)(-5(color(red)(x))-6y=3 color(white)("ddd")->color(white)("ddd")-5(color(red)((8y)/3-7/3))-6y=3 )`

`color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-(40y)/3+35/3color(white)("dd")-6y=3 )`

Put everything over 3 to make calculation more straight forward.

`color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-(40y)/3+35/3color(white)("dd")-(18y)/3=9/3 )`

Multiply both sides by 3

`color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-40y+35color(white)("dd")-18y=9`

`-58y=-26`

`y=+13/29`
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I will let you finish off