So I guess I have to:
Solve the system using any algebraic method.
I'm not sure how so here is the problem I'm stuck on.
9x-5y=-30
x+2y=-3
In the second equation, subtract the 2y to get x=-2y-3. Then plug you new value for x into the first equation:
9(-2y-3)- 5y = -30. Find the answer for y and then plug it into either equation to get the answer for x.
Ummm....huh?? I am more of a visual learner so maybe if it was worked out completly it would help a little more.
make the second equation, x+2y = -3, into x = -3-2y and substitute -3-2y into the first equation, 9x-5y. then, you will get 9(-3-2y)-5y = -30. that should simplify to -27 - 18y - 5y = -30. That should simplify to -27 - 23y = -30. that simplifies to -23y = -3. Therefore, y = 3/23.
In the second equation, x+2y = -3, substitute 3/23 for y. (x + 2 (3/23))= -3. that simplifies to x + 6/23 = -3. therefore, x = -3 6/23.
To solve this system of equations using algebraic methods, you can use either the substitution method or the elimination method. I will explain both methods so that you can choose the one you are more comfortable with or find simpler to use.
Method 1: Substitution method
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation, solve for x in terms of y:
x = -2y - 3
Step 2: Substitute the expression found in Step 1 into the other equation.
Replace x in the first equation with (-2y - 3):
9(-2y - 3) - 5y = -30
Step 3: Simplify and solve the resulting equation for the remaining variable.
Distribute the 9 to the terms inside the parentheses:
-18y - 27 - 5y = -30
Combine the like terms:
-23y - 27 = -30
Add 27 to both sides of the equation:
-23y = -3
Divide both sides by -23:
y = 3/23
Step 4: Substitute the value of y back into one of the original equations to solve for the other variable.
Using the second equation:
x + 2(3/23) = -3
Multiply 2 by 3/23:
x + 6/23 = -3
Subtract 6/23 from both sides of the equation:
x = -3 - 6/23
x = (-69 - 6)/23
x = -75/23
So the solution to the system of equations is x = -75/23 and y = 3/23.
Method 2: Elimination method
Step 1: Multiply one or both equations by suitable constants to make the coefficients of one of the variables the same or additive inverses.
In this case, it is easier to eliminate x. Multiply the second equation by 9 so that the coefficients of x in both equations are the same:
9(x + 2y) = 9(-3)
9x + 18y = -27
Step 2: Subtract the two equations to eliminate the variable.
(9x + 18y) - (9x - 5y) = -27 - (-30)
9x + 18y - 9x + 5y = -27 + 30
Simplify:
23y = 3
Step 3: Solve the resulting equation for the remaining variable.
Divide both sides by 23:
y = 3/23
Step 4: Substitute the value of y back into one of the original equations to solve for the other variable.
Using the first equation:
9x - 5(3/23) = -30
Multiply 5 by 3/23:
9x - 15/23 = -30
Add 15/23 to both sides of the equation:
9x = -30 + 15/23
Combine the terms on the right side:
9x = (-690 + 15)/23
9x = -675/23
Divide both sides by 9:
x = -675/207
Thus, the solution to the system of equations is x = -675/207 and y = 3/23.
I hope this explanation helps you understand how to solve the given system of equations using algebraic methods!