solve by the elimination method:
9x-9y=18
7y-3x=-8
please solve step by step
thank you for your help
Multiply second equation by 3.
21y-9x = 24
Add the two equations.
12y = 42
I hope you can take it from here.
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Choose one equation and multiply it by a constant to make the coefficients of either x or y the same in both equations. In this case, we'll choose the second equation to multiply by 3 to make the coefficients of x the same.
Multiply the second equation by 3:
(3) * (7y - 3x) = (3) * (-8)
21y - 9x = -24
Now we have 9x in the first equation and -9x in the second equation, making it easier to eliminate x.
Step 2: Multiply one or both equations by constants so that when you add or subtract them, one variable will be eliminated. In this case, we'll multiply the first equation by -3 to make -9x in the second equation become 9x.
Multiply the first equation by -3:
(-3) * (9x - 9y) = (-3) * (18)
-27x + 27y = -54
Step 3: Now, add the two modified equations together, which will result in the elimination of the x variable.
Combine the two equations:
-27x + 27y + 21y - 9x = -54 - 24
Simplify the equation:
-27x - 9x + 27y + 21y = -78
Combine like terms:
-36x + 48y = -78
Step 4: Now we have a new equation with only y. Solve this equation for y.
Rearrange the equation:
48y = 36x - 78
Divide both sides of the equation by 48:
y = (36x - 78) / 48
Simplify if possible:
y = (3x - 13) / 4
Step 5: Substitute the value of y back into one of the original equations. Let's use the first equation.
Substitute (3x - 13) / 4 for y in the first equation:
9x - 9((3x - 13) / 4) = 18
Multiply through by 4 to eliminate the fraction:
36x - 9(3x - 13) = 72
Distribute 9 to terms inside the parentheses:
36x - 27x + 117 = 72
Combine like terms:
9x + 117 = 72
Subtract 117 from both sides:
9x = -45
Divide both sides by 9:
x = -5
Step 6: Substitute the value of x back into one of the original equations to find the corresponding value of y. Let's use the second equation.
Substitute -5 for x in the second equation:
7y - 3(-5) = -8
Simplify:
7y + 15 = -8
Subtract 15 from both sides:
7y = -23
Divide both sides by 7:
y = -23/7
So, the solution to the system of equations is x = -5 and y = -23/7.