Eliminate y: Step 1: Use elimination method to eliminate y. Multiply the first equation by 5 and the second by 4: (9x + 4y) * 5 = 5 * 5, (4x - 5y) * 4 = 9 * 4.Simplify equations: Step 2: Simplify the equations: 45x + 20y = 25, 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: x = 61 / 61, 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: 4y = 5 - 9, 4y = -4, y = -4 / 4, y = -1.

Grade 7

Solve equations involving like terms

Full solution

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: $\newline$ $4y = 5 - 9$ , $\newline$ $4y = -4$ , $\newline$ $y = -4 / 4$ , $\newline$ $y = -1$ .