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Solve the system of equations. $\newline$ $y=-2$ $\newline$ $4x-3y=18$

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Solve equations involving like terms

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Q. Solve the system of equations.

\newline

y=-2

\newline

4x-3y=18

Identify Equations: Identify the given equations. $\newline$ We are given two equations: $y = -2$ and $4x - 3y = 18$ . The first equation is already solved for $y$ , which makes it easier to substitute into the second equation.
Substitute $y$ in Second: Substitute the value of $y$ from the first equation into the second equation. $\newline$ Since $y = -2$ , we can replace $y$ in the second equation with $-2$ . This gives us $4x - 3(-2) = 18$ .
Simplify and Solve for x: Simplify the equation and solve for x. $\newline$ $4x + 6 = 18$ (because $-3 \times -2 = 6$ ). $\newline$ Now, subtract $6$ from both sides to isolate the term with $x$ . $\newline$ $4x + 6 - 6 = 18 - 6$ $\newline$ $4x = 12$ $\newline$ Next, divide both sides by $4$ to solve for $x$ . $\newline$ $\frac{4x}{4} = \frac{12}{4}$ $\newline$ $x = 3$
Check Solution: Check the solution in both original equations. $\newline$ First, check $y = -2$ . Since we did not change $y$ , it remains $-2$ , which is correct. $\newline$ Second, check $4x - 3y = 18$ with $x = 3$ and $y = -2$ . $\newline$ $4(3) - 3(-2) = 12 + 6 = 18$ , which is true.

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