Question

Solve this system of equations. {3x+4y=36{y=-1/2x+8After solving, graph the equations

Answer 1

`x=(24)/(5)`
`y=(28)/(5)`

Step-by-step explanation

Step 1

Let

`\begin{gathered} 4x+3y=36\text{ Equation(1)} \\ y=-(1)/(2)x+8\text{ Equation(2)} \end{gathered}`

Step 2

replace equation(2) in equation(1)

so

`\begin{gathered} 4x+3y=36\text{ Equation(1)} \\ 4x+3(-(1)/(2)x+8)=36\text{ } \\ \text{operate} \\ 4x-(3)/(2)x+24=36 \\ \text{Add similar terms} \\ (5)/(2)x+24=36 \\ \text{subtract 24 in both sides} \\ (5)/(2)x+24-24=36-24 \\ (5)/(2)x=12 \\ \text{Multiply both sides by }(2)/(5) \\ (5)/(2)x\cdot(2)/(5)=12\cdot(2)/(5) \\ x=(24)/(5) \end{gathered}`

Step 3

`\begin{gathered} y=-(1)/(2)x+8\text{ Equation(2)} \\ y=-(1)/(2)((24)/(5))+8\text{ } \\ y=-(24)/(10)+8 \\ y=-(12)/(5)+8 \\ y=(28)/(5) \\ \end{gathered}`

replace x in equation (2).

I hope this helps you