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Solve the following system of equations.

{:[x+2y=10],[-x-5y=-22]:}

Solve the following system of equations. $\newline$ $x+2y=10$ $\newline$ $-x-5y=-22$ $\newline$

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Quotient property of logarithms

Full solution

Q. Solve the following system of equations.

\newline

x+2y=10

\newline

-x-5y=-22

\newline

Add Equations: Step $1$ : Add the two equations to eliminate $x$ . $\newline$ Equation $1$ : $x + 2y = 10$ $\newline$ Equation $2$ : $-x - 5y = -22$ $\newline$ Add them: $(x - x) + (2y - 5y) = 10 - 22$ $\newline$ Result: $-3y = -12$
Solve for y: Step $2$ : Solve for y. $\newline$ Divide both sides by $-3$ : $y = -12 / -3$ $\newline$ $y = 4$
Substitute to find $x$ : Step $3$ : Substitute $y = 4$ into the first equation to find $x$ . $x + 2(4) = 10$ $x + 8 = 10$ $x = 10 - 8$ $x = 2$

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