Solve using elimination. –4x − 3y = 7 –2x − 3y = –7 (_____, _____)

Write Equations: Write down the system of equations. –4x − 3y = 7 –2x − 3y = –7Multiply Second Equation: Multiply the second equation by 2 to make the coefficients of x in both equations the same. 2 * (–2x − 3y) = 2 * (–7) This gives us: –4x − 6y = –14New System of Equations: Now we have the system of equations: –4x − 3y = 7 –4x − 6y = –14Eliminate x: Subtract the second equation from the first equation to eliminate x. (–4x − 3y) − (–4x − 6y) = 7 − (–14) This simplifies to: 0x + 3y = 21Solve for y: Solve for y. 3y = 21 y = 21 / 3 y = 7Substitute and Find x: Substitute y = 7 into one of the original equations to find x. Using the first equation: –4x − 3y = 7 –4x − 3(7) = 7 –4x − 21 = 7Isolate x: Add 21 to both sides of the equation to isolate the term with x. –4x − 21 + 21 = 7 + 21 –4x = 28Solve for x: Divide both sides by -4 to solve for x. –4x / -4 = 28 / -4 x = –7

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Solve using elimination. $\newline$ $-4x - 3y = 7$ $\newline$ $-2x - 3y = -7$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-4x - 3y = 7

\newline

-2x - 3y = -7

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-4x - 3y = 7$ $\newline$ $-2x - 3y = -7$
Multiply Second Equation: Multiply the second equation by $2$ to make the coefficients of $x$ in both equations the same. $\newline$ $2 \times (–2x − 3y) = 2 \times (–7)$ $\newline$ This gives us: $\newline$ $–4x − 6y = –14$
New System of Equations: Now we have the system of equations: $\newline$ $-4x - 3y = 7$ $\newline$ $-4x - 6y = -14$
Eliminate x: Subtract the second equation from the first equation to eliminate x. $\newline$ $(-4x - 3y) - (-4x - 6y) = 7 - (-14)$ $\newline$ This simplifies to: $\newline$ $0x + 3y = 21$
Solve for y: Solve for y. $\newline$ $3y = 21$ $\newline$ $y = \frac{21}{3}$ $\newline$ $y = 7$
Substitute and Find $x$ : Substitute $y = 7$ into one of the original equations to find $x$ . Using the first equation: $–4x − 3y = 7$ $–4x − 3(7) = 7$ $–4x − 21 = 7$
Isolate x: Add $21$ to both sides of the equation to isolate the term with $x$ . $\newline$ $-4x - 21 + 21 = 7 + 21$ $\newline$ $-4x = 28$
Solve for x: Divide both sides by $-4$ to solve for x. $\newline$ $-4x / -4 = 28 / -4$ $\newline$ $x = -7$