Question

Please include work!

Answer 1

x = ± 4

y = - 2

Explanation:

y = 0.5x² - 10 ------------------------(I)

y = -x² + 14 ------------------------(II)

Substitute the y value in equation (II)

0.5x² - 10 = -x² + 14 {Add x² to both sides}

0.5x² + x² -10 = 14 {combine like terms}

1.5x² - 10 = 14 {Add 10 to both sides}

1.5x² = 14 + 10

1.5x² = 24 {Divide both sides by 1.5}

1.5x²/1.5 = 24/1.5

x² = 16

x = ±4

Substitute x = 4 in (I)

y = 0.5 * 4² - 10

= 0.5*16 - 10

= 8- 10

y = -2

Substitute x = -4 in (I)

y = 0.5 * (-4)² - 10

= 0.5*16 - 10

= 8- 10

y = -2