Question

Sole this system by substitution . X+y=6 and y=3x-2. Find the ordered pair

Answer 1

`(2,4)`Step-by-step explanation

given the system

`\begin{gathered} x+y=6\Rightarrow equation(1) \\ y=3x-2\Rightarrow equation(2) \end{gathered}`

Step 1

a) substitute the y value from equationi (2) into equation(1) , then solve for x

so

`\begin{gathered} x+y=6 \\ replace\text{ the y value from equation \lparen2\rparen} \\ x+(3x-2)=6 \\ add\text{ like terms} \\ 4x-2=6 \\ add\text{ 2 in both sides} \\ 4x-2+2=6+2 \\ 4x=8 \\ divide\text{ both sides by 4} \\ (4x)/(4)=(8)/(4) \\ x=2 \end{gathered}`

so

x=2

Step 2

now, replace the x value in equation (1) and solve for y

`\begin{gathered} x+y=6\Rightarrow equation(1) \\ replace\text{ the x value and solve for y} \\ 2+y=6 \\ subtract\text{ 2 in both sides} \\ 2+y-2=6-2 \\ y=4 \end{gathered}`

so

y=4

so, the ordered pair

`(2,4)`

I hope this helps you