Solve using elimination: {[5x+4y=-9],[4x-3y=30]:}

Align Equations for Elimination: Step 1: Align the equations for elimination. Equations given: 1) 5x + 4y = -9 2) 4x - 3y = 30 We aim to eliminate one variable by making the coefficients of y equal in magnitude but opposite in sign. Multiply to Align Coefficients: Step 2: Multiply the first equation by 3 and the second by 4 to align the y coefficients. (5x + 4y) * 3 = -9 * 3 → 15x + 12y = -27 (4x - 3y) * 4 = 30 * 4 → 16x - 12y = 120 Now, the y coefficients are 12 and -12, which can be eliminated by addition. Add Equations to Eliminate: Step 3: Add the modified equations to eliminate y. 15x + 12y + 16x - 12y = -27 + 120 31x = 93 Now, solve for x: x = 93 / 31 x = 3 Substitute and Solve: Step 4: Substitute x = 3 back into one of the original equations to find y. Using the first equation: 5x + 4y = -9 5(3) + 4y = -9 15 + 4y = -9 4y = -9 - 15 4y = -24 y = -24 / 4 y = -6

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Solve using elimination: $\newline$ $5x+4y=-9, \ 4x-3y=30$

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination:

\newline

5x+4y=-9, \ 4x-3y=30

Align Equations for Elimination: Step $1$ : Align the equations for elimination. $\newline$ Equations given: $\newline$ $1$ ) $5x + 4y = -9$ $\newline$ $2$ ) $4x - 3y = 30$ $\newline$ We aim to eliminate one variable by making the coefficients of $y$ equal in magnitude but opposite in sign.
Multiply to Align Coefficients: Step $2$ : Multiply the first equation by $3$ and the second by $4$ to align the $y$ coefficients. $\newline$ $(5x + 4y) \times 3 = -9 \times 3 \rightarrow 15x + 12y = -27$ $\newline$ $(4x - 3y) \times 4 = 30 \times 4 \rightarrow 16x - 12y = 120$ $\newline$ Now, the $y$ coefficients are $12$ and $-12$ , which can be eliminated by addition.
Add Equations to Eliminate: Step $3$ : Add the modified equations to eliminate $y$ . $\newline$ $15x + 12y + 16x - 12y = -27 + 120$ $\newline$ $31x = 93$ $\newline$ Now, solve for $x$ : $\newline$ $x = \frac{93}{31}$ $\newline$ $x = 3$
Substitute and Solve: Step $4$ : Substitute $x = 3$ back into one of the original equations to find $y$ . Using the first equation: $5x + 4y = -9$ $5(3) + 4y = -9$ $15 + 4y = -9$ $4y = -9 - 15$ $4y = -24$ $y = -24 / 4$ $y = -6$