Solve this system using substitution and give your answer as a point: 3x + 2y = 42 and x = (1/2)y.

Answer 1

Lysandra, you have two simultaneous equations (the "system") in two variables, x and y:

(1) 3x + 2y = 42 and (2) x = 1/2 y

Substitution means that you substitute one equation into the other. The second equation tells us x, so we can immediately replace this for the x in the first equation.

Hence, 3x + 2y = 42 becomes 3(1/2 y) + 2y = 42 (which is now an equation in only one variable, y).

This simplifies to 3/2 y + 2y = 42

=> 7/2 y = 42

=> 7y = 84

=> y = 12

Now you have the y value, use equation (2) to get x.

x = 1/2 y = 1/2(12) = 6

Hence the point is (6,12)

As always, it's good to double-check your answer. So I'll put those values into equation (1).

3x + 2y = 42

3(6) = 18 and 2(12) = 24 and 18+24 = 42 which is what we want.

Answer 2

Substitute

(3/2)y + 2y =42

Clear fractions

3y + 4y = 42

Divide by 7

y=6

x=3