Question

Solve the following simultaneous equation by using an algebraic method (either substitution or elimination)

Answer 1

Answer:

( $\frac{29}{14}$, - $\frac{19}{7}$)

Step-by-step explanation:

given the 2 equations

2x + 3y = - 4 → (1)

4x - y = 11 → (2)

Rearrange (2) expressing y in terms of x, that is

y = 4x - 11 → (3)

Substitute y = 4x - 11 into (1)

2x + 3(4x - 11) = - 4

2x + 12x - 33 = - 4

14x - 33 = - 4 ( add 33 to both sides )

14x = 29 ( divide both sides by 14 )

x = $\frac{29}{14}$

Substitute this value into (3) for corresponding value of y

y = (4 × $\frac{29}{14}$) - 11 = $\frac{116}{14}$ - $\frac{154}{14}$ = - $\frac{38}{14}$ = - $\frac{19}{7}$

solution is ( $\frac{29}{14}$, - $\frac{19}{7}$)