Question

14.2: theyre like terms, man
rewrite each expression by combining like terms.

1. 11s - 2s
2. 5t + 3z - 2t
3. 23s - (13t + 7t)
4. 7t + 18r + (2r - 5t)
5. -4x + 6r - (7x + 2r)
6. 3(c - 5) + 2c
7. 8x - 3y + (3y - 5x)
8. 5x + 4y - (5x + 7y)
9. 9x - 2y - 3(3x + y)
10. 6x + 12y + 2(3x - 6y)

14.3: finding more lines
for each system of equations:

• solve the system of equations by graphing. write the solution as an ordered pair.
• write an equation that would represented by a vertical or horizontal line that also passes through the solution of the system of equations.
• graph your new equation along with the system.

1. \\(\

$$\begin{cases} y = 3x + 5 \\\\ y = -x + 1 \\end{cases}$$

\\) the line representing \\(y = 3x + 5\\) is shown
graph: a coordinate grid with the line \\(y = 3x + 5\\) plotted, with x and y axes from -10 to 10

Explanation:

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14.2: Combining Like Terms

Step1: Combine like terms for 1

$11s - 2s = (11-2)s$

Step2: Combine like terms for 2

$5t - 2t + 3z = (5-2)t + 3z$

Step3: Simplify parentheses for 3

$23s -13t -7t = 23s + (-13-7)t$

Step4: Group like terms for 4

$7t -5t +18r +2r = (7-5)t + (18+2)r$

Step5: Simplify parentheses for 5

$-4x -7x +6r -2r = (-4-7)x + (6-2)r$

Step6: Distribute and combine for 6

$3c -15 +2c = (3+2)c -15$

Step7: Eliminate opposites for 7

$8x -5x -3y +3y = (8-5)x + (-3+3)y$

Step8: Simplify parentheses for 8

$5x -5x +4y -7y = (5-5)x + (4-7)y$

Step9: Distribute and combine for 9

$9x -9x -2y -3y = (9-9)x + (-2-3)y$

Step10: Distribute and combine for 10

$6x +6x +12y -12y = (6+6)x + (12-12)y$

Step1: Solve system algebraically

Set $3x+5 = -x+1$
$3x + x = 1 -5$
$4x = -4$
$x = -1$
Substitute $x=-1$: $y = -(-1)+1=2$

Step2: Write vertical/horizontal line

Vertical line: $x=-1$; Horizontal line: $y=2$

Step3: Graph verification

Plot $y=-x+1$ (y-intercept 1, slope -1). It intersects $y=3x+5$ at $(-1,2)$.

Answer:

1. $9s$
2. $3t + 3z$
3. $23s - 20t$
4. $2t + 20r$
5. $-11x + 4r$
6. $5c - 15$
7. $3x$
8. $-3y$
9. $-5y$
10. $12x$

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14.3: System of Equations