Solve using elimination. –6x + 7y = –16 x + 7y = 19 (_____, _____)

Align Equations for Elimination: Step 1: Align the equations for elimination. Given equations: –6x + 7y = –16 x + 7y = 19 We aim to eliminate y by making the coefficients of y in both equations equal and opposite. Multiply the second equation by 6. Calculation: 6(x + 7y) = 6(19) 6x + 42y = 114Add Equations to Eliminate y: Step 2: Add the modified second equation to the first equation to eliminate y. –6x + 7y = –16 6x + 42y = 114 Adding these equations: (–6x + 6x) + (7y + 42y) = –16 + 114 0x + 49y = 98Solve for y: Step 3: Solve for y. 49y = 98 y = 98 / 49 y = 2Substitute to Find x: Step 4: Substitute y = 2 back into one of the original equations to find x. Using the second equation: x + 7y = 19 x + 7(2) = 19 x + 14 = 19 x = 19 - 14 x = 5

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Solve using elimination. $\newline$ $-6x + 7y = -16$ $\newline$ $x + 7y = 19$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-6x + 7y = -16

\newline

x + 7y = 19

\newline

(_____, _____)

Align Equations for Elimination: Step $1$ : Align the equations for elimination. $\newline$ Given equations: $\newline$ $-6x + 7y = -16$ $\newline$ $x + 7y = 19$ $\newline$ We aim to eliminate $y$ by making the coefficients of $y$ in both equations equal and opposite. Multiply the second equation by $6$ . $\newline$ Calculation: $6(x + 7y) = 6(19)$ $\newline$ $6x + 42y = 114$
Add Equations to Eliminate $y$ : Step $2$ : Add the modified second equation to the first equation to eliminate $y$ . $\newline$ $-6x + 7y = -16$ $\newline$ $6x + 42y = 114$ $\newline$ Adding these equations: $\newline$ $(–6x + 6x) + (7y + 42y) = –16 + 114$ $\newline$ $0x + 49y = 98$
Solve for y: Step $3$ : Solve for y. $\newline$ $49y = 98$ $\newline$ $y = \frac{98}{49}$ $\newline$ $y = 2$
Substitute to Find $x$ : Step $4$ : Substitute $y = 2$ back into one of the original equations to find $x$ . Using the second equation: $x + 7y = 19$ $x + 7(2) = 19$ $x + 14 = 19$ $x = 19 - 14$ $x = 5$