Question

Solve the system of linear equations.-x+y=4x+3y=4

Answer 1

x=-2

y=2

Step-by-step explanation

`\begin{gathered} -x+y=4\text{ Equation(1)} \\ x+3y=4\text{ Equation(2)} \end{gathered}`

Step 1

isolate y in equation (1) and replace in equation (2)

`\begin{gathered} -x+y=4\text{ Equation(1)} \\ \text{add x in both sides} \\ -x+y+x=4+x \\ y=4+x\Rightarrow Equation(3) \end{gathered}`

now, replace equation (3) in equation(2)

`\begin{gathered} x+3y=4\text{ Equation(2)} \\ x+3(4+x)=4\text{ } \\ x+12+3x=4 \\ 12+4x=4 \\ \text{subtract 12 in both sides} \\ 12+4x-12=4-12 \\ 4x=-8 \\ \text{divide both sides by 4} \\ (4x)/(4)=-(8)/(4) \\ x=-2 \end{gathered}`

Step 2

now replace the x value in equation (3) to find y

`\begin{gathered} y=4+x\Rightarrow Equation(3) \\ y=4+(-2) \\ y=4-2 \\ y=2 \end{gathered}`

I hope this helps you