Solve using elimination. –6x + 4y = 12 –7x + 4y = 18 (_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: –6x + 4y = 12 –7x + 4y = 18 Since the coefficients of y are the same, we can subtract one equation from the other to eliminate y.Subtract equations: Subtract the first equation from the second equation: (–7x + 4y) - (–6x + 4y) = 18 - 12 This simplifies to: –7x + 4y - (–6x) - 4y = 18 - 12Simplify equation: Simplify the equation by combining like terms: –7x + 6x = 18 - 12 This results in: –x = 6Find x value: To find the value of x, we divide both sides by –1: –x / –1 = 6 / –1 This gives us: x = –6Substitute x into equation: Now that we have the value of x, we can substitute it into one of the original equations to find the value of y. Let's use the first equation: –6x + 4y = 12 Substitute x = –6 into the equation: –6(–6) + 4y = 12Perform multiplication: Perform the multiplication: 36 + 4y = 12Subtract to solve for y: Subtract 36 from both sides to solve for y: 4y = 12 - 36 4y = –24Divide to find y: Divide both sides by 4 to find the value of y: y = –24 / 4 y = –6

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Solve using elimination. $\newline$ $-6x + 4y = 12$ $\newline$ $-7x + 4y = 18$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-6x + 4y = 12

\newline

-7x + 4y = 18

\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: $\newline$ $-6x + 4y = 12$ $\newline$ $-7x + 4y = 18$ $\newline$ Since the coefficients of $y$ are the same, we can subtract one equation from the other to eliminate $y$ .
Subtract equations: Subtract the first equation from the second equation: $\newline$ $(-7x + 4y) - (-6x + 4y) = 18 - 12$ $\newline$ This simplifies to: $\newline$ $-7x + 4y - (-6x) - 4y = 18 - 12$
Simplify equation: Simplify the equation by combining like terms: $\newline$ $-7x + 6x = 18 - 12$ $\newline$ This results in: $\newline$ $-x = 6$
Find x value: To find the value of x, we divide both sides by $–1$ : $\frac{–x}{–1} = \frac{6}{–1}$ This gives us: $x = –6$
Substitute $x$ into equation: Now that we have the value of $x$ , we can substitute it into one of the original equations to find the value of $y$ . Let's use the first equation: $\newline$ $-6x + 4y = 12$ $\newline$ Substitute $x = -6$ into the equation: $\newline$ $-6(-6) + 4y = 12$
Perform multiplication: Perform the multiplication: $36 + 4y = 12$
Subtract to solve for y: Subtract $36$ from both sides to solve for $y$ : $\newline$ $4y = 12 - 36$ $\newline$ $4y = -24$
Divide to find $y$ : Divide both sides by $4$ to find the value of $y$ :
$y = -\frac{24}{4}$
$y = -6$