Question

GIFT is a rectangle with GT= -3x + 5y, GS= 3x+y, IF = 11, and IS = 13 What is the value of x and y

Answer 1

we have:

GT = IF

GS = IS

therefore we have the following system of equations:

`\begin{gathered} -3x+5y=11 \\ 3x+y=13 \end{gathered}`

and solve for x and y

`\begin{gathered} 3x+y=13 \\ 3x+y-3x=13-3x \\ y=13-3x \\ -3x+5(13-3x)=11 \\ -3x+65-15x=11 \\ -18x+65=11 \\ -18x+65-65=11-65 \\ -18x=-54 \\ (-18x)/(-18)=-(54)/(-18) \\ x=3 \end{gathered}`

and for y:

`\begin{gathered} y=13-3x \\ y=13-3(3) \\ y=13-9 \\ y=4 \end{gathered}`

answer:

x = 3

y = 4