Solve the following simultaneous equation using the elimination method:

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1. Solve the following simultaneous equation using the elimination method:
The given equations are:

2x + 3y = 12 \quad \text{(i)}

3x - y = 7 \quad \text{(ii)}

Multiply equation (ii) by 3 to make the coefficients of $y$ opposites.
$3 \times (3x - y) = 3 \times 7$ $9x - 3y = 21 \quad \text{(iii)}$
Add equation (i) and equation (iii) to eliminate $y$ .
$(2x + 3y) + (9x - 3y) = 12 + 21$ $11x = 33$
Solve for $x$ .
$x = \frac{33}{11}$ $x = 3$
Substitute the value of $x=3$ into equation (ii) to solve for $y$ .
$3(3) - y = 7$ $9 - y = 7$ $-y = 7 - 9$ $-y = -2$ $y = 2$
The solution is $\boxed{x=3, y=2}$ .

2. Write 0.00456 to 4 significant figures.
Identify the first non-zero digit.
The first non-zero digit in 0.00456 is 4.
Count four significant figures starting from the first non-zero digit.
The significant figures are 4, 5, 6. This is only 3 significant figures.
To express the number to 4 significant figures, we add a trailing zero.
$0.004560$
The number 0.00456 to 4 significant figures is $\boxed{0.004560}$ .

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