Question

what is the solution to the system of equations?
2x - y = 7

y = 2x + 3

○ (2, 3)
○ (2, 7)
○ no solution
○ infinite number of solutions

Explanation:

Step1: Substitute \( y = 2x + 3 \) into \( 2x - y = 7 \)

Substitute the expression for \( y \) from the second equation into the first equation. So we get \( 2x - (2x + 3) = 7 \).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \( 2x-2x - 3=7 \), which simplifies to \( - 3=7 \).
Since \( - 3
eq7 \), this is a contradiction. When we have a contradiction in a system of linear equations, it means that the two lines represented by the equations are parallel and do not intersect. So the system of equations has no solution.

Answer:

no solution