Find x and y. {:[2x+8y=6],[5x+20 y=15]:}

Write Equations: Let's write down the system of equations we need to solve: {:[2x+8y=6],[5x+20y=15]:} We will first look for a way to simplify the equations, if possible.Simplify Equations: Notice that both equations have terms that can be simplified by dividing by a common factor. In the first equation, we can divide every term by 2, and in the second equation, we can divide every term by 5. Simplified system: {:[x+4y=3],[x+4y=3]:}Identify Identical Equations: After simplifying, we see that both equations are identical, which means they represent the same line. This implies that there are infinitely many solutions, and x and y are not uniquely determined by this system. Instead, they have a dependent relationship described by the equation x + 4y = 3.

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Math Problems

Grade 8

Write an equation word problem

Full solution

Q. Find

x

and

y

\newline

2x+8y=6 \newline

5x+20y=15

Write Equations: Let's write down the system of equations we need to solve: $\newline$ \begin{cases}2x+8y=6\5x+20y=15\end{cases} $\newline$ We will first look for a way to simplify the equations, if possible.
Simplify Equations: Notice that both equations have terms that can be simplified by dividing by a common factor. In the first equation, we can divide every term by $2$ , and in the second equation, we can divide every term by $5$ . Simplified system: $\begin{cases} x+4y=3 \ x+4y=3 \end{cases}$
Identify Identical Equations: After simplifying, we see that both equations are identical, which means they represent the same line. This implies that there are infinitely many solutions, and $x$ and $y$ are not uniquely determined by this system. Instead, they have a dependent relationship described by the equation $x + 4y = 3$ .