Solve using elimination. 4x + 10y = 4 4x + 8y = –4 (_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We can subtract the second equation from the first equation to eliminate the variable x. 4x + 10y = 4 -(4x + 8y = –4)Perform subtraction: Perform the subtraction of the two equations: (4x + 10y) - (4x + 8y) = 4 - (-4) This simplifies to: 4x - 4x + 10y - 8y = 4 + 4Simplify equation: Simplify the equation by combining like terms: 0x + 2y = 8 This simplifies to: 2y = 8Divide to solve y: Divide both sides of the equation by 2 to solve for y: 2y / 2 = 8 / 2 y = 4Substitute y into equation: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. We'll use the first equation: 4x + 10y = 4 Substitute y = 4 into the equation: 4x + 10(4) = 4Perform multiplication: Perform the multiplication: 4x + 40 = 4Subtract to solve x: Subtract 40 from both sides of the equation to solve for x: 4x + 40 - 40 = 4 - 40 4x = -36Divide to solve x: Divide both sides of the equation by 4 to solve for x: 4x / 4 = -36 / 4 x = -9

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Solve using elimination. $\newline$ $4x + 10y = 4$ $\newline$ $4x + 8y = -4$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

4x + 10y = 4

\newline

4x + 8y = -4

\newline

(_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We can subtract the second equation from the first equation to eliminate the variable $x$ . $4x + 10y = 4$ $-(4x + 8y = -4)$
Perform subtraction: Perform the subtraction of the two equations: $\newline$ $(4x + 10y) - (4x + 8y) = 4 - (-4)$ $\newline$ This simplifies to: $\newline$ $4x - 4x + 10y - 8y = 4 + 4$
Simplify equation: Simplify the equation by combining like terms: $\newline$ $0x + 2y = 8$ $\newline$ This simplifies to: $\newline$ $2y = 8$
Divide to solve $y$ : Divide both sides of the equation by $2$ to solve for $y$ : $\frac{2y}{2} = \frac{8}{2}$ $y = 4$
Substitute $y$ into equation: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . We'll use the first equation: $\newline$ $4x + 10y = 4$ $\newline$ Substitute $y = 4$ into the equation: $\newline$ $4x + 10(4) = 4$
Perform multiplication: Perform the multiplication: $4x + 40 = 4$
Subtract to solve $x$ : Subtract $40$ from both sides of the equation to solve for $x$ : $4x + 40 - 40 = 4 - 40$ $4x = -36$
Divide to solve $x$ : Divide both sides of the equation by $4$ to solve for $x$ : $\frac{4x}{4} = \frac{-36}{4}$ $x = -9$