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Solve using elimination. $\newline$ $-5x + 5y = 20$ $\newline$ $-10x + 5y = 5$ $\newline$ (_, _)

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Solve a system of equations using elimination

Full solution

Q. Solve using elimination.

\newline

-5x + 5y = 20

\newline

-10x + 5y = 5

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-5x + 5y = 20$ $\newline$ $-10x + 5y = 5$
Eliminate Variable: To use elimination, we need to eliminate one variable. We can subtract the second equation from the first equation to eliminate the $y$ variable. $(-5x + 5y) - (-10x + 5y) = 20 - 5$
Subtract Equations: Perform the subtraction. $\newline$ $-5x + 5y + 10x - 5y = 20 - 5$
Simplify Equation: Simplify the equation. $5x = 15$
Solve for x: Solve for x by dividing both sides by $5$ . $\frac{5x}{5} = \frac{15}{5}$ $x = 3$
Substitute $x$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the first equation. $\newline$ $-5(3) + 5y = 20$
Simplify Equation: Perform the multiplication and simplify the equation. $\newline$ $-15 + 5y = 20$
Add $15$ : Add $15$ to both sides to solve for $y$ . $\newline$ $5y = 20 + 15$ $\newline$ $5y = 35$
Divide by $5$ : Divide both sides by $5$ to find the value of y. $\newline$ $\frac{5y}{5} = \frac{35}{5}$ $\newline$ $y = 7$

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