Solve the simultaneous equation
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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Here are the given equations:
$$6x - y = 22 \quad (1)$$
$$6x + 5y = -2 \quad (2)$$
Step 1: Subtract equation (1) from equation (2) to eliminate $x$.
$$(6x + 5y) - (6x - y) = -2 - 22$$
$$6x + 5y - 6x + y = -24$$
$$6y = -24$$
Step 2: Solve for $y$.
$$\frac{6y}{6} = \frac{-24}{6}$$
$$y = -4$$
Step 3: Substitute the value of $y = -4$ into equation (1).
$$6x - (-4) = 22$$
$$6x + 4 = 22$$
Step 4: Solve for $x$.
$$6x = 22 - 4$$
$$6x = 18$$
$$\frac{6x}{6} = \frac{18}{6}$$
$$x = 3$$
The solution is $x=3$ and $y=-4$.
$$\boxed{x=3, y=-4}$$
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