Answer
$$x=7$$ $$y=2$$
Work Step by Step
Equation 1: $3(2x + y) = 4x + 20$
Equation 2: $x - 2y = 3$
Simplify equation 1:
$$3(2x + y) = 4x + 20$$ $$6x + 3y = 4x + 20$$
Subtract $4x$ from both sides:
$$6x-4x + 3y = 4x-4x + 20$$ $$2x + 3y = 20$$
This will be equation 1'.
Using equation 2, add $2y$ to both sides:
$$x - 2y = 3$$ $$x - 2y+2y = 3+2y$$ $$x=3+2y$$
Substitute this equation to equation 1':
$$2x + 3y = 20$$ $$2(3+2y)+ 3y = 20$$ $$6+4y+ 3y = 20$$ $$6+7y = 20$$
Subtract $6$ from both sides:
$$6-6+7y = 20-6$$ $$7y = 14$$
Divide both sides by $7$:
$$\frac{7y}{7} = \frac{14}{7}$$ $$y=2$$
Substitute this value of $y$ to equation 2:
$$x - 2y = 3$$ $$x - 2(2) = 3$$ $$x - 4 = 3$$
Add $4$ to both sides:
$$x - 4+4 = 3+4$$ $$x=7$$
Use equation 1 to check:
$$3(2x + y) = 4x + 20$$ $$3(2(7) + 2) = 4(7) + 20$$ $$3(14 + 2) = 28 + 20$$ $$3(16) = 48$$ $$48=48$$
