Solve this simultaneous linear and quadratic equation by using subtraction method, 2x-y=8 3x-y=17
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
Step 1: Write down the given equations.
$$2x - y = 8 \quad \text{(1)}$$
$$3x - y = 17 \quad \text{(2)}$$
Step 2: Subtract equation (1) from equation (2) to eliminate $y$.
$$(3x - y) - (2x - y) = 17 - 8$$
$$3x - y - 2x + y = 9$$
$$x = 9$$
Step 3: Substitute the value of $x$ into equation (1) to solve for $y$.
$$2(9) - y = 8$$
$$18 - y = 8$$
$$-y = 8 - 18$$
$$-y = -10$$
$$y = 10$$
The solution is $x=9$ and $y=10$.
$$\boxed{x=9, y=10}$$
