Question

What is the solution of the linear quadratic system of equations?

y−x=x 2 +5x−3
Y-X=2
​A) No solution
B) x=−1,y=6
C) x=1,y=−4
D) x=−3,y=2

Answer 1

The correct solution of the system is (x, y) = (0, -3), by first isolating y in the linear equation and then substituting this into the quadratic equation.

Step-by-step explanation:

The solution of the linear quadratic system of equations can be found by substitution or elimination. Given that y - x = x² + 5x - 3 is a combined system with a linear equation and a quadratic equation, we first express y in terms of x from the linear equation and then substitute into the quadratic equation to solve for x.

First, rewriting the linear equation in terms of y, we get:
y = x² + 6x - 3. Now, since y - x = x² + 5x - 3, equating the two expressions for y gives us x² + 6x - 3 = x² + 5x - 3. Simplifying, we get x = 0 as the solution for x. Substituting x back into the equation for y gives us y = -3. However, none of the given options match the solution (x = 0, y = -3), which implies there might be an error in the options given or the question itself.