Question

hive me a place to stand. and i will move the earth.-3 4 5 -7 6 7-1-1 -4 2 7 -5 1 8 -5 -5-3 9 1 8(a,c) $x+y=-3LXB0x-y=10$(g,h) $x+y=0LXB12x-y=-13$(m,n) $x+2y=4LXB22x-y=6$(r,s) $2x+y=21LXB3x-y=10$(v,w) $2x+y=20$$x-y=1$what is your answer?in your own words, how can you use substitution to solve a system

Explanation:

Step1: Solve (A,C) system via elimination

We have:

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

Add the two equations:
$x + y + x - y = -3 + (-3)$
$2x = -6$
$x = -3$
Substitute $x=-3$ into $x+y=-3$:
$-3 + y = -3$
$y = 0$
Pair (A,C) → $(-3,0)$

Step2: Solve (D,E) system via elimination

We have:

$$\begin{cases} x + y = 0 \\ x - y = 10 \end{cases}$$

Add the two equations:
$x + y + x - y = 0 + 10$
$2x = 10$
$x = 5$
Substitute $x=5$ into $x+y=0$:
$5 + y = 0$
$y = -5$
Pair (D,E) → $(5,-5)$

Step3: Solve (G,H) system via elimination

We have:

$$\begin{cases} x + y = 0 \\ x - y = -16 \end{cases}$$

Add the two equations:
$x + y + x - y = 0 + (-16)$
$2x = -16$
$x = -8$
Substitute $x=-8$ into $x+y=0$:
$-8 + y = 0$
$y = 8$
Pair (G,H) → $(-8,8)$

Step4: Solve (I,L) system via elimination

We have:

$$\begin{cases} x + 2y = -9 \\ 2x - y = -13 \end{cases}$$

Multiply the second equation by 2:
$4x - 2y = -26$
Add to the first equation:
$x + 2y + 4x - 2y = -9 + (-26)$
$5x = -35$
$x = -7$
Substitute $x=-7$ into $x+2y=-9$:
$-7 + 2y = -9$
$2y = -2$
$y = -1$
Pair (I,L) → $(-7,-1)$

Step5: Solve (M,N) system via elimination

We have:

$$\begin{cases} x + 2y = 4 \\ 2x - y = -12 \end{cases}$$

Multiply the second equation by 2:
$4x - 2y = -24$
Add to the first equation:
$x + 2y + 4x - 2y = 4 + (-24)$
$5x = -20$
$x = -4$
Substitute $x=-4$ into $x+2y=4$:
$-4 + 2y = 4$
$2y = 8$
$y = 4$
Pair (M,N) → $(-4,4)$

Step6: Solve (O,P) system via elimination

We have:

$$\begin{cases} x + 2y = -2 \\ 2x - y = 6 \end{cases}$$

Multiply the second equation by 2:
$4x - 2y = 12$
Add to the first equation:
$x + 2y + 4x - 2y = -2 + 12$
$5x = 10$
$x = 2$
Substitute $x=2$ into $x+2y=-2$:
$2 + 2y = -2$
$2y = -4$
$y = -2$
Pair (O,P) → $(2,-2)$

Step7: Solve (R,S) system via elimination

We have:

$$\begin{cases} 2x + y = 21 \\ x + y = 8 \end{cases}$$

Subtract the second equation from the first:
$2x + y - (x + y) = 21 - 8$
$x = 13$
Substitute $x=13$ into $x+y=8$:
$13 + y = 8$
$y = -5$
Pair (R,S) → $(13,-5)$

Step8: Solve (T,U) system via elimination

We have:

$$\begin{cases} 2x + y = -7 \\ x - y = 10 \end{cases}$$

Add the two equations:
$2x + y + x - y = -7 + 10$
$3x = 3$
$x = 1$
Substitute $x=1$ into $x-y=10$:
$1 - y = 10$
$y = -9$
Pair (T,U) → $(1,-9)$

Step9: Solve (V,W) system via elimination

We have:

$$\begin{cases} 2x + y = 20 \\ x - y = 1 \end{cases}$$

Add the two equations:
$2x + y + x - y = 20 + 1$
$3x = 21$
$x = 7$
Substitute $x=7$ into $x-y=1$:
$7 - y = 1$
$y = 6$
Pair (V,W) → $(7,6)$

Step10: Map coordinates to letters

Using the provided number-letter key:

• $(-3,0)$ → S
• $(5,-5)$ → I
• $(-8,8)$ → H
• $(-7,-1)$ → P
• $(-4,4)$ → E
• $(2,-2)$ → A
• $(13,-5)$ → C
• $(1,-9)$ → E
• $(7,6)$ → D

Answer:

The decoded phrase is HID A PIECE (ordered by the coordinate pairs mapped to their corresponding letters)