Question

Solve the system. Use any method you w y=2x+3 11x²+y²=9

Answer 1

To solve the system, substitute y=2x+3 into the second equation to find two possible values for x: 0 and -4/5. Substituting these x values back into the first equation yields the corresponding y values, resulting in two solutions: (0,3) and (-4/5,1.5).

Step-by-step explanation:

To solve the system of equations, we can substitute the expression from the first equation into the second equation. Given:

• y=2x+3
• 11x²+y²=9

We substitute the expression for y from the first equation into the second equation:

(2x+3)² = y²

11x² + (2x+3)² = 9

Now expand the squared term:

11x² + (4x² + 12x + 9) = 9

15x² + 12x + 9 = 9

This simplifies to:

15x² + 12x = 0

x(15x + 12) = 0

Now we solve for x:

• x = 0
• 15x + 12 = 0
• x = -⅔

With the values of x, we can find corresponding y values by substituting back into the first equation:

For x = 0:

y = 2(0) + 3

y = 3

For x = -⅔:

y = 2(-⅔) + 3

y = 3 - 1⅒

y = 1⅒

Thus, the system has two solutions: (0, 3) and (-⅔, 1⅒).