Solve the following simultaneous equations. 3×+4y=−6 2× −9=24 5×−2y=1 −18×=36y 3×+2y=8 ×=6y

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the three sets of simultaneous equations you provided.

System 1:

3x+4y=-6

2x-9=24

Solve the second equation for $x$ .
$2x-9=24$ $2x = 24+9$ $2x = 33$ $x = \frac{33}{2}$ $x = 16.5$
Substitute the value of $x$ into the first equation and solve for $y$ .
$3(16.5)+4y=-6$ $49.5+4y=-6$ $4y = -6-49.5$ $4y = -55.5$ $y = \frac{-55.5}{4}$ $y = -13.875$
The solution for the first system is $\boxed{x=16.5, y=-13.875}$ .

System 2:
$5x-2y=1$ $-18x=36y$
Simplify the second equation to express $y$ in terms of $x$ .
$-18x=36y$ $\frac{-18x}{36} = y$ $y = -\frac{1}{2}x$
Substitute this expression for $y$ into the first equation and solve for $x$ .
$5x-2\left(-\frac{1}{2}x\right)=1$ $5x+x=1$ $6x=1$ $x=\frac{1}{6}$
Substitute the value of $x$ back into the simplified expression for $y$ .
$y = -\frac{1}{2}\left(\frac{1}{6}\right)$ $y = -\frac{1}{12}$
The solution for the second system is $\boxed{x=\frac{1}{6}, y=-\frac{1}{12}}$ .

System 3:
$3x+2y=8$ $x=6y$
Substitute the expression for $x$ from the second equation into the first equation.
$3(6y)+2y=8$ $18y+2y=8$ $20y=8$
Solve for $y$ .
$y=\frac{8}{20}$ $y=\frac{2}{5}$
Substitute the value of $y$ back into the second equation to find $x$ .
$x=6\left(\frac{2}{5}\right)$ $x=\frac{12}{5}$
The solution for the third system is $\boxed{x=\frac{12}{5}, y=\frac{2}{5}}$ .

Solve the following simultaneous equations. 3×+4y=-6 2× -9=24 5×-2y=1 −18×=36y 3×+2y=8 ×=6y