Solve the simultaneous equations. $\frac{x}{4}-\frac{y}{2}=2$ $3x=19+4y$ You must show your working. Answer x = ... y = ...

1. Clear the fractions in the first equation.

$\frac{x}{4}-\frac{y}{2}=2$
Multiply throughout by $4$:
$x-2y=8$

2. Write both equations in comparable linear form.

From $3x=19+4y,$
subtract $4y$ from both sides:
$3x-4y=19$
So the equations are
$x-2y=8 \quad \text{and} \quad 3x-4y=19.$

3. Eliminate $x$ to find $y$.

Multiply $x-2y=8$ by $3$:
$3x-6y=24$
Subtract $3x-4y=19$:

4. Substitute $y$ back to find $x$.

Substitute $y=-\dfrac{5}{2}$ into $x-2y=8$:
$x-2\left(-\frac{5}{2}\right)=8$
$x+5=8$
$x=3$