Question

Use substitution to solve.

2x² = 5 + y
4y = -20 + 8x²

Solve the first equation for y and substitute it into the second equation. The resulting equation is
✔ 8x² - 20 = -20 + 8x²
.
The system has
.

Answer 1

From 2x² = 5 + y, solve for y: y = 2x² − 5.
Substitute into 4y = −20 + 8x²: 4(2x² − 5) = −20 + 8x² → 8x² − 20 = −20 + 8x².

This identity holds for all x, so the system has infinitely many solutions: all pairs (x, y) with y = 2x² − 5 (x any real number).