Question

How many solutions does the following system of equations have?

2y=5x+4
y=3x+2

a) infinitely many
b) zero
c) one
d) two

Answer 1

Option c is correct

One solution does the following system of equations have

Explanation:

Given the system of equation:

`2y = 5x+4` ....[1]

`y=3x+2` ....[2]

Substitute equation [2] into [1] we have;

`2(3x+2) = 5x+4`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`6x+4 = 5x+4`

Subtract 4 from both sides we have;

`6x = 5x`

Subtract 5x from both sides we have;

`x = 0`

Substitute this in equation [2] we have;

y = 3(0)+2

y = 2

Therefore, the solution of the given system of equation is: (0, 2)

Answer 2

The system:
2 y = 5 x + 4
y = 3 x + 2
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We will substitute y in the 1st equation:
2 ( 3 x + 2 ) = 5 x + 4
6 x + 4 = 5 x + 4
6 x - 5 x = 4 - 4
x = 0
Answer: C ) one solution.