Solve using elimination. 5x + 10y = 15 5x + 8y = 11 (_____, _____)

System of Equations: System of equations: 5x + 10y = 15 5x + 8y = 11 Which variable should we eliminate? Since the coefficient of x is the same in both equations, we will eliminate x.Eliminate Variable: System of equations: 5x + 10y = 15 5x + 8y = 11 Which operation should we use to eliminate x? Coefficients of x: 5 and 5 Here the coefficients are the same, we should subtract the second equation from the first.Subtract Equations: Subtract the second equation from the first to eliminate x. (5x + 10y) - (5x + 8y) = 15 - 11 5x + 10y - 5x - 8y = 4 10y - 8y = 4 2y = 4Solve for y: Solve for y. Divide both sides of the equation by 2. 2y / 2 = 4 / 2 y = 2Substitute and Solve: Substitute y = 2 into one of the original equations to solve for x. Let's use the first equation 5x + 10y = 15. 5x + 10(2) = 15 5x + 20 = 15 5x = 15 - 20 5x = -5Solve for x: Solve for x. Divide both sides of the equation by 5. 5x / 5 = -5 / 5 x = -1Final Solution: We found: x = -1 y = 2 Write the solution as a coordinate point. Solution: (-1, 2)

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Solve using elimination. $\newline$ $5x + 10y = 15$ $\newline$ $5x + 8y = 11$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

5x + 10y = 15

\newline

5x + 8y = 11

\newline

(_____, _____)

System of Equations: System of equations: $\newline$ $5x + 10y = 15$ $\newline$ $5x + 8y = 11$ $\newline$ Which variable should we eliminate? $\newline$ Since the coefficient of $x$ is the same in both equations, we will eliminate $x$ .
Eliminate Variable: System of equations: $\newline$ $5x + 10y = 15$ $\newline$ $5x + 8y = 11$ $\newline$ Which operation should we use to eliminate $x$ ? $\newline$ Coefficients of $x$ : $5$ and $5$ $\newline$ Here the coefficients are the same, we should subtract the second equation from the first.
Subtract Equations: Subtract the second equation from the first to eliminate $x$ .
$(5x + 10y) - (5x + 8y) = 15 - 11$
$5x + 10y - 5x - 8y = 4$
$10y - 8y = 4$
$2y = 4$
Solve for y: Solve for y. $\newline$ Divide both sides of the equation by $2$ . $\newline$ $\frac{2y}{2} = \frac{4}{2}$ $\newline$ $y = 2$
Substitute and Solve: Substitute $y = 2$ into one of the original equations to solve for $x$ . Let's use the first equation $5x + 10y = 15$ .
$5x + 10(2) = 15$
$5x + 20 = 15$
$5x = 15 - 20$
$5x = -5$
Solve for x: Solve for x. $\newline$ Divide both sides of the equation by $5$ . $\newline$ $\frac{5x}{5} = \frac{-5}{5}$ $\newline$ $x = -1$
Final Solution: We found: $\newline$ $x = -1$ $\newline$ $y = 2$ $\newline$ Write the solution as a coordinate point. $\newline$ Solution: $(-1, 2)$