answer:
To solve the system of equations:
3x - y = 17
-2x - 3y = -4
We can use the method of substitution or elimination.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, solve for y:
y = 3x - 17
Step 2: Substitute the expression for y into the other equation.
Replace y in the second equation with 3x - 17:
-2x - 3(3x - 17) = -4
Step 3: Simplify and solve for x.
-2x - 9x + 51 = -4
-11x + 51 = -4
-11x = -4 - 51
-11x = -55
x = -55 / -11
x = 5
Step 4: Substitute the value of x back into either equation to solve for y.
Using the first equation:
3(5) - y = 17
15 - y = 17
-y = 17 - 15
-y = 2
y = -2
So, the solution to the system of equations is x = 5 and y = -2.
Method 2: Elimination
Step 1: Multiply the equations by appropriate constants to make the coefficients of one variable opposite in sign.
Multiply the first equation by 3 and the second equation by -1:
9x - 3y = 51
2x + 3y = 4
Step 2: Add the equations together to eliminate one variable.
(9x - 3y) + (2x + 3y) = 51 + 4
11x = 55
x = 55 / 11
x = 5
Step 3: Substitute the value of x back into either equation to solve for y.
Using the first equation:
3(5) - y = 17
15 - y = 17
-y = 17 - 15
-y = 2
y = -2
So, the solution to the system of equations is x = 5 and y = -2.
Both methods give the same solution: x = 5 and y = -2.
~~Alli~~