Answer
Hence, the solution to this system is $(0.27,1.57)$,This is a consistent system with independent lines.
Work Step by Step
The given system is
$7d+4r=8.17$ ...... (1)
$2r=8d+0.98$ ...... (2)
Divide equation (2) by $2$.
$r=4d+0.49$ ...... (3)
Substitute the value of $r$ from equation (3) to equation (1).
$7d+4(4d+0.49)=8.17$
Use the distributive property.
$7d+16d+1.96=8.17$
Add like terms.
$23d+1.96=8.17$
Subtract $1.96$ from both sides.
$23d+1.96-1.96=8.17-1.96$
Simplify.
$23d=6.21$
Divide both sides by $23$.
$\frac{23d}{23}=\frac{6.21}{23}$
Simplify.
$d=0.27$
Substitute the value of $d$ into equation (3).
$r=4(0.27)+0.49$
Clear the parentheses.
$r=1.08+0.49$
Add.
$r=1.57$.
Check $d=0.27$ and $r=1.57$ into equation (1).
$7(0.27)+4(1.57)=8.17$
$1.89+6.28=8.17$
$8.17=8.17$ True.
Check $d=0.27$ and $r=1.57$ into equation (2).
$2(1.57)=8(0.27)+0.98$
$3.14=2.16+0.98$
$3.14=3.14$ True.
