Question

Algebra 1!!

x=2y and 2x+3y=21
-solve the given system of equations by substitution
answers-
a. x=6, y=-3
b. x=6, y=3
c. x=3, y=3
d. x=3, y=6

Answer 1

`\huge\boxed{b.\ x=6;\ y=3}`

Explanation:

`\left\{\begin{array}{ccc}x=2y&(1)\\2x+3y=21&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\2(2y)+3y=21\\4y+3y=21\qquad\text{combine like terms}\\7y=21\qquad\text{divide both sides by 7}\\(7y)/(7)=(21)/(7)\\\boxed{y=3}\\\\\text{Substitute it to (1):}\\x=2(3)\\\boxed{x=6}`

Answer 2

Answer: (6, 3)

Explanation: Our first equation tells us that x means the same thing as 2y so we can replace the x in the second equation with a 2y.

Our second equation then becomes 2(2y) + 3y = 21.

If we simplify on the left side we get

4y + 3y = 21 which simplifies to 7y = 21.

Solving from here, we find that y = 3.

To find x, plug 3 back in for y in the first equation

to get x = 2(3) which simplifies to x = 6.

So our answer is (6, 3).