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

Where do the following equations intersect?

$\left( \frac{10}{21} , \frac{557}{21} \right)$

$\left( \frac{17}{14} , \frac{557}{21} \right)$

$\left( -41 , \frac{557}{21} \right)$

$\left( \frac{17}{14} , 74 \right)$

$\left( \frac{17}{14} , \frac{157}{21} \right)$

Explanation

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.

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

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

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

Where do the following equations intersect?

$\left( \frac{21}{19} , - \frac{312}{19} \right)$

$\left( \frac{1}{9} , - \frac{312}{19} \right)$

$\left( \frac{2}{21} , - \frac{312}{19} \right)$

$\left( \frac{1}{9} , -28 \right)$

$\left( \frac{1}{9} , - \frac{207}{19} \right)$

Explanation

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.

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

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

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

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

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

Where do the following equations intersect?

$\left( - \frac{17}{27} , - \frac{419}{27} \right)$

$\left( - \frac{7}{17} , - \frac{419}{27} \right)$

$\left( - \frac{23}{4} , - \frac{419}{27} \right)$

$\left( - \frac{7}{17} , -62 \right)$

$\left( - \frac{7}{17} , - \frac{827}{27} \right)$

Explanation

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.

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

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

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

Where do the following equations intersect?

$\left( - \frac{3}{35} , - \frac{361}{35} \right)$

$\left( \frac{29}{35} , - \frac{361}{35} \right)$

$\left( - \frac{43}{27} , - \frac{361}{35} \right)$

$\left( \frac{29}{35} , -38 \right)$

$\left( \frac{29}{35} , - \frac{493}{35} \right)$

Explanation

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.

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

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

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

Where do the following equations intersect?

$\left( 2 , 21 \right)$

$\left( -\infty , 21 \right)$

$\left( - \frac{10}{7} , 21 \right)$

$\left( -\infty , 45 \right)$

$\left( -\infty , 43 \right)$

Explanation

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 divide by on each side.

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

$y = -10 \cdot 2 + 41$

Where do the following equations intersect?

$\left( \frac{3}{70} , \frac{2187}{70} \right)$

$\left( - \frac{1}{74} , \frac{2187}{70} \right)$

$\left( - \frac{29}{41} , \frac{2187}{70} \right)$

$\left( - \frac{1}{74} , 51 \right)$

$\left( - \frac{1}{74} , \frac{2103}{70} \right)$

Explanation

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.

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

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

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

Where do the following equations intersect?

$\left( - \frac{40}{89} , - \frac{447}{89} \right)$

$\left( \frac{32}{17} , - \frac{447}{89} \right)$

$\left( - \frac{49}{40} , - \frac{447}{89} \right)$

$\left( \frac{32}{17} , 3 \right)$

$\left( \frac{32}{17} , \frac{1473}{89} \right)$

Explanation

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:

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

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

Where do the following equations intersect?

$\left( \frac{23}{88} , \frac{637}{88} \right)$

$\left( \frac{64}{47} , \frac{637}{88} \right)$

$\left( - \frac{45}{43} , \frac{637}{88} \right)$

$\left( \frac{64}{47} , 13 \right)$

$\left( \frac{64}{47} , \frac{1695}{88} \right)$

Explanation

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.

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

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

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

Where do the following equations intersect?

$\left( \frac{17}{22} , -30 \right)$

$\left( \frac{23}{16} , -30 \right)$

$\left( - \frac{1}{2} , -30 \right)$

$\left( \frac{23}{16} , -65 \right)$

$\left( \frac{23}{16} , - \frac{1017}{22} \right)$

Explanation

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.

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

Where do the following equations intersect?

$\left( - \frac{13}{28} , - \frac{239}{28} \right)$

$\left( \frac{7}{8} , - \frac{239}{28} \right)$

$\left( 29 , - \frac{239}{28} \right)$

$\left( \frac{7}{8} , -61 \right)$

$\left( \frac{7}{8} , - \frac{629}{28} \right)$

Explanation

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.

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

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

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

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

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

Use Graph Points to Approximate Solutions: CCSS.Math.Content.HSA-REI.D.11

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