Solving linear systems of substitution

1 answer:

6 0

Example: 2x+2y=8 and 3y+2x=6
Okay so u first want to put on of the equations into a y= form. So let's use 3y+2x=6. Subtract 2x from both sides. 3y=6-2x divide by 3. Y= 6-2/3x or y= -2/3x + 6. Now just plug this new equation in for Y since "y=" into the other equation.
2x + 2(-2/3x + 6) = 8.
Then you would distribute the 2 into the parenthesis and simplify to solve for x.
After you solve for x, plug x into one of the original equations to find y.

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<u>Solution:</u>

Given that , In a certain function, y varies directly with x

And x = 8 when y = 6,

We have to find what will be the value of x when y = 9

Now, from the given information,

$\begin{array}{l}{y \alpha x} \\\\ {y=c x \rightarrow(1)}\end{array}$

where c is the proportionality constant

$\begin{array}{l}{\text { Now, substitute } x=8 \text { and } y=6 \text { in }(1)} \\\\ {\rightarrow 8=c(6) \rightarrow c=\frac{8}{6}} \\\\ {\rightarrow c=\frac{4}{3}} \\\\ {\text { Then, }(1) \rightarrow x=\frac{4}{3} y} \\\\ {\text { So, when } y=9} \\\\ {\rightarrow x=\frac{4}{3}(9)} \\\\ {\rightarrow x=4 \times 3} \\\\ {\rightarrow x=12}\end{array}$

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