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Solve the system of equations by using the substitution method. $\newline$ $-4x+7y=20$ $\newline$ $Y= 3x+15$ $\newline$ $X=$ _ $Y=$ _

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Solve polynomial equations

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Q. Solve the system of equations by using the substitution method.

\newline

-4x+7y=20

\newline

Y= 3x+15

\newline

X=

_______

Y=

_______

Substitute and Simplify: Step $1$ : Substitute the expression for $y$ from the second equation into the first equation. $\newline$ Given: $\newline$ $-4x + 7y = 20$ $\newline$ $y = 3x + 15$ $\newline$ Substitute $y$ : $\newline$ $-4x + 7(3x + 15) = 20$
Distribute and Combine: Step $2$ : Distribute and combine like terms. $\newline$ $-4x + 21x + 105 = 20$ $\newline$ $17x + 105 = 20$
Solve for x: Step $3$ : Solve for x. $\newline$ Subtract $105$ from both sides: $\newline$ $17x = -85$ $\newline$ Divide by $17$ : $\newline$ $x = -5$
Substitute for y: Step $4$ : Substitute $x = -5$ back into the second equation to find $y$ . $y = 3(-5) + 15$ $y = -15 + 15$ $y = 0$

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