Practice section 1 of 4

Solve the following systems of linear equations without using a graphing calculator. (a) $2x+y=3$, $4x-3y=0$. (b) $x+y+z=6$, $x+2y+z=8$, $2x+y+z=7$.

Solve Example 1(b) using a graphing calculator: $x+y+z=6$, $x+2y+z=8$, $2x+y+z=7$.

Solve $x+2y+3z=1$, $2x+4y+6z=2$, $2x+3y+z=3$.

Solve $x+2y-2z=3$, $x+3z=-6$, $5x+3y-z=2$, $3x-2y+z=0$.

[Banking] Stephen inherited $50,000 and put part in an investment-savings account, part in bonds and the rest in an investment fund. After one year he received a total of $3,240 in simple interest. The account paid 6% annually, bonds 7% and the fund 8%. There was $12,000 more invested in bonds than in the fund. Find the amount invested in each category.

[Conics] A circle has equation $x^2+y^2+Ax+By+C=0$. Find its equation if it passes through $(3,-1)$, $(-2,4)$ and $(6,8)$. State its centre and radius.