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{:[y=5x+3],[2y=18 x-10]:}

$\begin{array}{c}y=5 x+3 \\ 2 y=18 x-10\end{array}$

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Write an equation word problem

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Q.

\begin{array}{c}y=5 x+3 \\ 2 y=18 x-10\end{array}

Given Equations: We are given a system of linear equations: $\newline$ ${y=5x+3}, {2y=18x-10}$ $\newline$ Our goal is to find the values of $x$ and $y$ that satisfy both equations simultaneously.
Express $y$ in terms of $x$ : First, let's use the first equation to express $y$ in terms of $x$ : $y = 5x + 3$
Substitute into second equation: Now, let's substitute the expression for $y$ from the first equation into the second equation: $2(5x + 3) = 18x - 10$
Distribute and simplify: Next, we distribute the $2$ on the left side of the equation: $2 \times 5x + 2 \times 3 = 18x - 10$ $10x + 6 = 18x - 10$
Rearrange terms: Now, we'll move all terms involving $x$ to one side and constant terms to the other side: $10x - 18x = -10 - 6$ $-8x = -16$
Find $x$ : To find the value of $x$ , we divide both sides of the equation by $-8$ : $x = \frac{{-16}}{{-8}}$ $x = 2$
Substitute $x$ into first equation: Now that we have the value of $x$ , we can substitute it back into the first equation to find $y$ : $y = 5(2) + 3$ $y = 10 + 3$ $y = 13$

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