Solve {l}{+t*(-2)=1+r*(-1)}{t*(-2)=-1-t}

$$\left. \begin{array}{l}{ + t \cdot ( - 2 ) = 1 + r \cdot ( - 1 ) }\\{ t \cdot ( - 2 ) = - 1 - t }\end{array} \right.$$

Solve for t, r

$$r=3$$

$$t=1$$

Solution Steps

Consider the second equation. Add t to both sides.

$$t\left(-2\right)+t=-1$$

Combine t\left(-2\right) and t to get -t.

$$-t=-1$$

Divide both sides by -1.

$$t=\frac{-1}{-1}$$

Divide -1 by -1 to get 1.

$$t=1$$

Consider the first equation. Insert the known values of variables into the equation.

$$1\left(-2\right)=1+r\left(-1\right)$$

Multiply 1 and -2 to get -2.

$$-2=1+r\left(-1\right)$$

Swap sides so that all variable terms are on the left hand side.

$$1+r\left(-1\right)=-2$$

Subtract 1 from both sides.

$$r\left(-1\right)=-2-1$$

Subtract 1 from -2 to get -3.

$$r\left(-1\right)=-3$$

Divide both sides by -1.

$$r=\frac{-3}{-1}$$

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$r=3$$

The system is now solved.

$$t=1 r=3$$