Question

Solve each system of the new equations by adding or subtracting

Answer 1

Given the equations

x + y = 5----------------------(1)

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

Subtract equation (2) from (1)

x - x -3y - y = 3 - 5

-4y = -2

Divide both -4

`\begin{gathered} (-4y)/(-4)\text{ = }(-2)/(-4) \\ y\text{ = }(1)/(2)\text{ = 0.5} \\ \end{gathered}`

Substitute y = 1/2 into equation (1)

x + y = 5

`\begin{gathered} x\text{ + }(1)/(2)\text{ =5} \\ x\text{ = 5 -}(1)/(2) \\ x\text{ = }(10-1)/(2) \\ x=(9)/(2)\text{ = 4.5} \\ \end{gathered}`

Hence, the solution to the equations is

`\begin{gathered} x\text{ = }4.5,\text{ y = 0.5} \\ Or\text{ in coordinate form, (4.5, 0.5)} \end{gathered}`