Question

Solve the sysyem of equations 3x+y=3 x+y=2

Answer 1

{x = 1/2 , y = 3/2

Explanation:

Solve the following system:

{3 x + y = 3 | (equation 1)

{x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x + y = 3 | (equation 1)

{0 x+(2 y)/3 = 1 | (equation 2)

Multiply equation 2 by 3:

{3 x + y = 3 | (equation 1)

{0 x+2 y = 3 | (equation 2)

Divide equation 2 by 2:

{3 x + y = 3 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Subtract equation 2 from equation 1:

{3 x+0 y = 3/2 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 1/2 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Collect results:

Answer: {x = 1/2 , y = 3/2

Answer 2

`\large\boxed{x=(1)/(2)\ and\ y=1(1)/(2)\to\left((1)/(2),\ 1(1)/(2)\right)}`

Explanation:

`\left\{\begin{array}{ccc}3x+y=3\\x+y=2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+y=3\\-x-y=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=1\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=(1)/(2)}\\\\\text{Put the value of x to the second equation:}\\(1)/(2)+y=2\qquad\text{subtract}\ (1)/(2)\ \text{from both sides}\\\boxed{y=1(1)/(2)}`