Rewriting Linear Equations in Standard Form (A) - Free Printable

To solve these problems, we need to rearrange each equation into the Standard Form of a linear equation.

The standard form looks like this:
$Ax + By = C$

Where:
- $A$, $B$, and $C$ are integers (whole numbers).
- $A$ (the number in front of $x$) should usually be positive.
- All the variables ($x$ and $y$) are on the left side.
- The constant number is on the right side.

Let's go through each problem step-by-step.

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Problem 1: $y + 2 = -5x$

1. Goal: Get $x$ and $y$ on the left, numbers on the right.
2. Add $5x$ to both sides to move the $x$ term.
$$5x + y + 2 = 0$$
3. Subtract $2$ from both sides to move the number.
$$5x + y = -2$$
4. Identify A, B, C: $A=5$, $B=1$, $C=-2$.

Problem 2: $-9 = -4x - 7y$

1. Goal: Get $x$ and $y$ on the left side.
2. Add $4x$ and $7y$ to both sides.
$$4x + 7y - 9 = 0$$
3. Add $9$ to both sides.
$$4x + 7y = 9$$
4. Identify A, B, C: $A=4$, $B=7$, $C=9$.

Problem 3: $8y + 5 = 5x$

1. Goal: Get variables on the left.
2. Subtract $5x$ from both sides.
$$-5x + 8y + 5 = 0$$
3. Subtract $5$ from both sides.
$$-5x + 8y = -5$$
4. *Note:* In standard form, we prefer $A$ to be positive. Multiply the whole equation by $-1$.
$$5x - 8y = 5$$
5. Identify A, B, C: $A=5$, $B=-8$, $C=5$.

Problem 4: $3x = 8 - 6y$

1. Goal: Get $y$ to the left side.
2. Add $6y$ to both sides.
$$3x + 6y = 8$$
3. The variables are already on the left and the number is on the right.
4. Identify A, B, C: $A=3$, $B=6$, $C=8$.

Problem 5: $-5 = 6y + x$

1. Goal: Put $x$ first, then $y$, then the number.
2. Rewrite the right side in order: $-5 = x + 6y$.
3. Flip the equation so variables are on the left.
$$x + 6y = -5$$
4. Identify A, B, C: $A=1$, $B=6$, $C=-5$.

Problem 6: $2x + 6 = 8y$

1. Goal: Get $y$ to the left side.
2. Subtract $8y$ from both sides.
$$2x - 8y + 6 = 0$$
3. Subtract $6$ from both sides.
$$2x - 8y = -6$$
4. Identify A, B, C: $A=2$, $B=-8$, $C=-6$.

Problem 7: $-4y - 8x = -4$

1. Goal: Put $x$ first, then $y$.
2. Rewrite: $-8x - 4y = -4$.
3. *Note:* We want $A$ to be positive. Multiply everything by $-1$.
$$8x + 4y = 4$$
4. Identify A, B, C: $A=8$, $B=4$, $C=4$.

Problem 8: $-7 = -2y - x$

1. Goal: Move variables to the left.
2. Add $2y$ and add $x$ to both sides.
$$x + 2y - 7 = 0$$
3. Add $7$ to both sides.
$$x + 2y = 7$$
4. Identify A, B, C: $A=1$, $B=2$, $C=7$.

Problem 9: $6y = 4x + 4$

1. Goal: Move $x$ to the left.
2. Subtract $4x$ from both sides.
$$-4x + 6y = 4$$
3. *Note:* Make $A$ positive by multiplying by $-1$.
$$4x - 6y = -4$$
4. Identify A, B, C: $A=4$, $B=-6$, $C=-4$.

Problem 10: $1 = -4x + 9y$

1. Goal: Move variables to the left.
2. Add $4x$ and subtract $9y$ from both sides.
$$4x - 9y + 1 = 0$$
3. Subtract $1$ from both sides.
$$4x - 9y = -1$$
4. Identify A, B, C: $A=4$, $B=-9$, $C=-1$.

Final Answer:
1. $5x + y = -2$; $A=5, B=1, C=-2$
2. $4x + 7y = 9$; $A=4, B=7, C=9$
3. $5x - 8y = 5$; $A=5, B=-8, C=5$
4. $3x + 6y = 8$; $A=3, B=6, C=8$
5. $x + 6y = -5$; $A=1, B=6, C=-5$
6. $2x - 8y = -6$; $A=2, B=-8, C=-6$
7. $8x + 4y = 4$; $A=8, B=4, C=4$
8. $x + 2y = 7$; $A=1, B=2, C=7$
9. $4x - 6y = -4$; $A=4, B=-6, C=-4$
10. $4x - 9y = -1$; $A=4, B=-9, C=-1$