Answer
The ordered pair $(-2,-4)$ is the solution of the system.
Work Step by Step
Equation 1: $3x - 4y = 10$
Equation 2: $y = 2x$
Substitute equation 2 to equation 1:
$$3x - 4y = 10$$ $$3x - 4(2x) = 10$$ $$3x - 8x = 10$$ $$-5x = 10$$
Divide both sides by $-5$:
$$\frac{-5x}{-5} = \frac{10}{-5}$$ $$x=-2$$
Substitute this value to equation 1:
$$3x - 4y = 10$$ $$3(-2) - 4y = 10$$ $$-6 - 4y = 10$$
Add $6$ to both sides:
$$-6+6 - 4y = 10+6$$ $$- 4y = 16$$
Divide both sides by $-4$:
$$\frac{-4y}{-4} = \frac{16}{-4}$$ $$y=-4$$
Check using equation 2:
$$y=2x$$ $$-4=2(-2)$$ $$-4=-4$$
Therefore, the ordered pair $(-2,-4)$ is the solution of the system.
