Question

3x + 8y = 28 3x + 2y = 4 Find both the x and y coordinates

Answer 1

Answer:

(- $\frac{4}{3}$, 4 )

Step-by-step explanation:

Given the 2 equations

3x + 8y = 28 → (1)

3x + 2y = 4 → (2)

Subtracting (2) from (1) term by term will eliminate the x- term

(3x - 3x) + (8y - 2y) = (28 - 4), that is

6y = 24 ( divide both sides by 6 )

y = 4

Substitute y = 4 into either of the 2 equations and solve for x

Substituting into (1)

3x + 8(4) = 28

3x + 32 = 28 ( subtract 32 from both sides )

3x = - 4 ( divide both sides by 3 )

x = - $\frac{4}{3}$

Solution is (- $\frac{4}{3}$, 4 )

Answer 2

If you subtract the two equations you get

$\underbrace{(3x + 8y)-(3x + 2y)}_{\text{Difference of the LHS}}=\underbrace{28-4}_{\text{Difference of the RHS}}$

This can be simplified into

$6y=24 \iff y=4$

Now you can plug this value for $y$ in one of the two equations, and solve it for $x$.