Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions,

express them in the ordered-pair form given in Example 6.

$\begin{array}{l}2x-6y=10\\ -3x+9y=-15\end{array}$

Short answer

Hence, the solution of the system of equations $\begin{array}{l}2x-6y=10\\ -3x+9y=-15\end{array}$ hasinfinitely many solution hence the ordered pair is $\left(t,\frac{t}{3}-\frac{5}{3}\right)$.

Step-by-step solution

Step 1. Given information.

Given a system of equations$\begin{array}{l}2x-6y=10\\ -3x+9y=-15\end{array}$

substitution method.

Step 2. Write down the concept.

Given equation,

$2x-6y=10$ …….(1)

$-3x+9y=-15$ …….(2)

Multiplying equation (1) by 3 and equation (2) by 2,

$6x-18y=30$ ……..(3)

Step 3. Determining the angle

Slope-intercept form of equation (2),

$\begin{array}{l}y=\frac{1}{9}\left(3x-15\right)\\ y=\frac{1}{3}x-\frac{5}{3}\end{array}$

Letting x=t,

$y=\frac{t}{3}-\frac{5}{3}$

Thus, the ordered pair is $\left(t,\frac{t}{3}-\frac{5}{3}\right)$.