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9x+4y=5,4x-5y=9

$9 x+4 y=5,4 x-5 y=9$

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Solve equations involving like terms

Full solution

Q.

9 x+4 y=5,4 x-5 y=9

Eliminate y: Step $1$ : Use elimination method to eliminate y. Multiply the first equation by $5$ and the second by $4$ : $(9x + 4y) \times 5 = 5 \times 5$ , $(4x - 5y) \times 4 = 9 \times 4$ .
Simplify equations: Step $2$ : Simplify the equations: $\newline$ $45x + 20y = 25$ , $\newline$ $16x - 20y = 36$ .
Add equations: Step $3$ : Add the two equations to eliminate $y$ : $45x + 20y + 16x - 20y = 25 + 36$ , $61x = 61$ .
Solve for x: Step $4$ : Solve for x: $\newline$ $x = \frac{61}{61}$ , $\newline$ $x = 1$ .
Substitute $x$ : Step $5$ : Substitute $x = 1$ into the first original equation to find $y$ : $9(1) + 4y = 5,$ $9 + 4y = 5.$
Solve for y: Step $6$ : Solve for y: $\newline$ $4y = 5 - 9$ , $\newline$ $4y = -4$ , $\newline$ $y = -4 / 4$ , $\newline$ $y = -1$ .

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