Use substitution to solve the quadratic-quadratic system of equations defined by:
1. x2 = 16 - y2
2. 12x2 + 25y2 - 400 = 0
Step 1:
| Determine which equation to substitute into which.
In this example, you will substitute Equation 1 into Equation 2. |
Step 2:
| Substitute the condition on x2 from Equation 1 into Equation 2.
12(16 - y2) + 25y2 - 400 = 0
| Step 3: | Expand and simplify:
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192 - 12y2 + 25y2 - 400 = 0
13y2 - 208 = 0
13y2 = 208
y2 = 16
y = ± Ö16
| y = ± 4
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Step 4:
| Substitute y = ± 4 into one of the original equations to find the corresponding y values.
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Let y = + 4 |
Let y = -4 |
| Then: x2 = 16 - (4)2 |
Then: x2 = 16 - (-4)2 |
| x2 = 16 - 16 |
x2 = 16 - 16 |
| x2 = 0 | x2 = 0 |
| x = 0 | x = 0 |
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| Thus the solutions of this system are (0, 4) and (0, -4)
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