Algebra - Equations - 3 Simultaneous equations.
Test Yourself 1.
Solve the following sets of 3 equations for the relevant 3 variables:
These are challenging but you could use them in parts of at least an advanced Mathematics course.
| 1:
x + 2y - z = -5 2x - 3y + 4z = 28 4x + 5y - 3z = -10 Hint.We could remove z by multiplying Eqn 1 by 4 to equate with Eqn 2 - then add.Then multiply Eqn 1 by 3 to equate to Eqn 3 - then subtract. The result is two equations in x and y - so proceed as usual. |
2:
e - f + g = 10 4e + 2f - 3g = 8 3e - 5f + 2g = 34 Hint.I suggest you work to eliminate g by forming two equations -in e and f. To form these two new equations, multiply Eqn 1 by 3 and then Eqn 1 by 2. |
3.
6x + 4y - 2z = 0 3x - 2y + 4z = 3 5x - 2y + 6z = 3 |
| 4:
2a - b - c = 9 5a + 2c = -3 7a - 2b = 1 |
5.
3p - q - 2r = -15 20p - 3q - 5r = -15 5p + 2q + 3r = -16 |
6.
x - 2y = 3 4y - 3z = 4 x + 3z = 2 |
| 1. The general form of a parabola could be written as
y = k(x - a)2 + b Given that the parabola passes through the points (-3, 7), (0, -5) and (2, -3), find the values of a, b and k and write down the equation of the parabola.
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