Jordan is solving this system of equations: y = 2x2 + 3 and y – x = 6. Which statements are true about Jordan’s system? Check all that apply.The quadratic equation is in standard form.Using substitution, the system of equations can be rewritten as 2x2 – x – 3 = 0. There are two real number solutions.There are no real number solutions. A solution of the system of equations is (–1, 1.5).

The quadratic is in standard form, y = ax² + bx + c: here a = 2, b = 0, and c = 3. From y − x = 6, we get y = x + 6; setting this equal to 2x² + 3 gives 2x² − x − 3 = 0. Its discriminant is (−1)² − 4(2)(−3) = 25, which is positive, so there are two real solutions. The point (−1, 1.5) is not a solution because when x = −1, the quadratic gives y = 5, not 1.5.

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