Use Graph Points to Approximate Solutions: CCSS.Math.Content.HSA-REI.D.11 - Common Core: High School - Algebra

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}.$

Subtract from both sides:

Add to both sides:

Divide both sides by $89\textup:$

$x = - \frac{40}{89}$

Now plug this $\uptext{x}$ value into one of the equations to solve for the $\uptext{y}$ value.

$y = 49 \cdot - \frac{40}{89} + 17$

Multiply $\frac{49}{1}$ by $-\frac{40}{89}\textup:$

$y = - \frac{1960}{89} + 17$

Make fractions with common denominators:

$\frac{17}{1}=\frac{1513}{89}$

Add fractions:

$y = - \frac{1960}{89} + \frac{1513}{89}$

$y = - \frac{447}{89}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

$x = \frac{23}{88}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -45 \cdot \frac{23}{88} + 19$

$y = - \frac{1035}{88} + 19$

$y = \frac{637}{88}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}.$

$x = \frac{17}{22}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 22 \cdot \frac{17}{22} -47$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we subtract from each side.

Now we add to each side.

Now we divide by on each side.

$x = \frac{4}{13}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 16 \cdot \frac{4}{13} + 22$

$y = \frac{64}{13} + 22$

$y = \frac{350}{13}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we subtract from each side.

Now we divide by on each side.

$x = - \frac{17}{27}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -23 \cdot - \frac{17}{27} -30$

$y = \frac{391}{27} -30$

$y = - \frac{419}{27}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we divide by on each side.

$x = \frac{62}{3}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 3 \cdot \frac{62}{3} -20$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we subtract from each side.

Now we subtract from each side.

Now we divide by on each side.

$x = \frac{55}{16}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -4 \cdot \frac{55}{16} + 20$

$y = - \frac{55}{4} + 20$

$y = \frac{25}{4}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we add to each side.

Now we divide by on each side.

$x = - \frac{13}{28}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -29 \cdot - \frac{13}{28} -22$

$y = \frac{377}{28} -22$

$y = - \frac{239}{28}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we subtract from each side.

Now we add to each side.

Now we divide by on each side.

$x = \frac{3}{70}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 29 \cdot \frac{3}{70} + 30$

$y = \frac{87}{70} + 30$

$y = \frac{2187}{70}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we add to each side.

Now we divide by on each side.

$x = \frac{29}{80}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 42 \cdot \frac{29}{80} -2$

$y = \frac{609}{40} -2$

$y = \frac{529}{40}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we subtract from each side.

Now we subtract from each side.

Now we divide by on each side.

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -10 \cdot 2 + 41$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we add to each side.

Now we divide by on each side.

$x = \frac{21}{19}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -4 \cdot \frac{21}{19} -12$

$y = - \frac{84}{19} -12$

$y = - \frac{312}{19}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we subtract from each side.

Now we add to each side.

Now we divide by on each side.

$x = \frac{10}{21}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 41 \cdot \frac{10}{21} + 7$

$y = \frac{410}{21} + 7$

$y = \frac{557}{21}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we subtract from each side.

Now we divide by on each side.

$x = - \frac{3}{35}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -43 \cdot - \frac{3}{35} -14$

$y = \frac{129}{35} -14$

$y = - \frac{361}{35}$

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Question

Where do the following equations intersect?

Answer

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

Now we add to each side.

Now we add to each side.

Now we divide by on each side.

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -8 \cdot -69 -43$

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