Question

How many solutions does the pair of equations x+2y=3 and x/2+y=3/2'?​

Answer 1

Answer:

System of equation has infinite solution.

Step-by-step explanation:

Given system of linear equation are:

x+2y-3=0x+2y−3=0

\frac{1}{2}x+y -\frac{3}{2}=0

2

1

x+y−

2

3

=0

We will check by

if \frac{a_1}{a_2}\neq\frac{b_1}{b_2}

a

2

a

1



=

b

2

b

1

then unique solution.

if \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

a

2

a

1

=

b

2

b

1

=

c

2

c

1

then infinite solution.

if \frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}

a

2

a

1

=

b

2

b

1



=

c

2

c

1

then no solution.

Now,

\frac{1}{\frac{1}{2}}=\frac{2}{1}=\frac{-3}{-\frac{3}{2}}

2

1

1

=

1

2

=

−

2

3

−3

2=2=22=2=2

Hence, system of equation has infinite solutions

Answer 2

Answer:

How many solutions does the pair of equations x+2y=3 and x/2+y=3/2'?​

Step-by-step explanation:

The equations are

x+2y=3

x/2+y=3/2

the second equation multiply by 2

this means the equation become x+2y=3 that is same as

equation one

hence both the equation are same

this means we have one equaiton and two variable

so we need to take one variable as arbitrory

hence the system has infinite many solutions.