Solve using elimination. 5x − 8y = 2 –7x + 8y = 10 (_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: 5x − 8y = 2 –7x + 8y = 10 We can see that the coefficients of y are opposites, which means we can add the two equations together to eliminate the y variable.Add Equations: Now, let's add the two equations together: (5x − 8y) + (–7x + 8y) = 2 + 10 This simplifies to: 5x − 7x = 12Combine Like Terms: Next, we combine like terms: −2x = 12Solve for x: Now, we solve for x by dividing both sides by -2: x = 12 / -2 x = -6Substitute x Value: With the value of x found, we can substitute x = -6 into one of the original equations to find the value of y. We'll use the first equation: 5x − 8y = 2 5(-6) − 8y = 2Perform Multiplication: Now, we perform the multiplication: -30 − 8y = 2Isolate y Term: Next, we add 30 to both sides to isolate the term with y: −8y = 2 + 30 −8y = 32Solve for y: Finally, we divide both sides by -8 to solve for y: y = 32 / -8 y = -4

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Solve using elimination. $\newline$ $5x - 8y = 2$ $\newline$ $-7x + 8y = 10$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

5x - 8y = 2

\newline

-7x + 8y = 10

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: $\newline$ $5x − 8y = 2$ $\newline$ $−7x + 8y = 10$ $\newline$ We can see that the coefficients of $y$ are opposites, which means we can add the two equations together to eliminate the $y$ variable.
Add Equations: Now, let's add the two equations together: $\newline$ $(5x − 8y) + (−7x + 8y) = 2 + 10$ $\newline$ This simplifies to: $\newline$ $5x − 7x = 12$
Combine Like Terms: Next, we combine like terms: $-2x = 12$
Solve for x: Now, we solve for x by dividing both sides by $-2$ : $\newline$ $x = \frac{12}{-2}$ $\newline$ $x = -6$
Substitute x Value: With the value of $x$ found, we can substitute $x = -6$ into one of the original equations to find the value of $y$ . We'll use the first equation: $\newline$ $5x − 8y = 2$ $\newline$ $5(-6) − 8y = 2$
Perform Multiplication: Now, we perform the multiplication: $\newline$ $-30 − 8y = 2$
Isolate y Term: Next, we add $30$ to both sides to isolate the term with $y$ : $\newline$ $-8y = 2 + 30$ $\newline$ $-8y = 32$
Solve for y: Finally, we divide both sides by $-8$ to solve for $y$ : $y = \frac{32}{-8}$ $y = -4$