The problem is to solve a system of two linear equations with two variables, $x$ and $y$. The equations are: $y = 2x - 3$ $2x - y = -4$

AlgebraLinear EquationsSystems of EquationsSubstitutionNo SolutionParallel Lines
2025/5/13

1. Problem Description

The problem is to solve a system of two linear equations with two variables, xx and yy. The equations are:
y=2x3y = 2x - 3
2xy=42x - y = -4

2. Solution Steps

We can use substitution to solve this system.
Since the first equation is already solved for yy, we can substitute the expression for yy from the first equation into the second equation.
Substitute y=2x3y = 2x - 3 into 2xy=42x - y = -4:
2x(2x3)=42x - (2x - 3) = -4
2x2x+3=42x - 2x + 3 = -4
3=43 = -4
This is a contradiction. Since 343 \neq -4, there is no solution to this system of equations. The two lines are parallel and do not intersect.

3. Final Answer

No solution.

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