# 1.4 Algebraic Manipulation

**The use of calculators or other technologies are strictly prohibited for this assignment.**

## 1 Solve for a Variable 

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a) Solve for $x$: $3 x + 3 = x + 7$

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b) Solve for $y$: $\frac{y}{2} = 2y - 6$

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c) Solve for $p$ in the equation $q = a - bp$.

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## 2 Solve a System of Equations

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a) Suppose you have a total of 900 five and ten dollar bills, and the value of that money is $5500. How many fives and tens do you have?

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   Let x be the number of fives and y be the number of tens.
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b) If $y = mx + b$ and $y = nx + c$, find the point of intersection (x, y) in terms of m, n, b, and c. Simplify: your final answer for y should be one term.

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