Question

Given the system of equations, what is the solution?

3x - 2y + 10 = 0
5y = 4x + 8

Answer 1

top equation, minus 10 both sides to get
3x-2y=-10

bottom equation, minus 4x both sides
5y-4x=8
-4x+5y=8

now elimiate y's


multiply top equation by 5 and bottom equaiton by 2 and add them together

15x-10y=-50
-8x+10y=16 +
7x+0y=-34

7x=-34
divide both sides by 7
x=-34/7

sub back

3x-2y=-10
3(-34/7)-2y=-10
(-102/7)-2y=-10
add (102/7) to both sides
-2y=-10+(102/7)
-2y=(-70/7)+(102/7)
-2y=32/7
divide both sides by -2, or times both sides by -1/2
y=-32/14
y=-16/7


(x,y)
(-34/7,-16/7)

Answer 2

Answer: The solutions are

`x=(-34)/(7)\\\\y=(-16)/(7)`

Explanation:

Since we have given that

3x - 2y + 10 = 0

5y = 4x + 8

So, it can be rewritten as :

3x-2y=-10---------------------(1)

4x-5y=-8----------------------(2)

Multiplying by 5 to eq(1) and 2 to eq(2).

`15x-10y=-50\\\\8x-10y=-16\\\\------------------------------------\\\\7x=-34\\\\x=(-34)/(7)`

And put the value of x in eq(1), to get the value of y:

`3* (-34)/(7)-2y=-10\\\\(-102)/(7)-2y=-10\\\\-2y=-10+(102)/(7)\\\\-2y=(-70+102)/(7)\\\\-2y=(32)/(7)\\\\y=(-16)/(7)`

Hence, the solutions are

`x=(-34)/(7)\\\\y=(-16)/(7)`