using substitution to solve
-3x+y= -17
2x-3y=23
y = (3 x - 17)
so
2 x - 3(3x-17) = 23
2x - 9 x + 51 = 23
7 x = 28
x = 4
so y = (3 x - 17) = 12-17 = -5
To solve this system of equations using substitution, we'll solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for y:
-3x + y = -17
Adding 3x to both sides:
y = 3x - 17
Now, substitute this expression for y in the second equation:
2x - 3(3x - 17) = 23
Simplify the equation by distributing the -3 to 3x and -17:
2x - 9x + 51 = 23
Combine like terms:
-7x + 51 = 23
Next, isolate the variable by subtracting 51 from both sides:
-7x = 23 - 51
Simplify:
-7x = -28
To find the value of x, divide both sides by -7:
x = -28 / -7
x = 4
Now that we have the value of x, substitute it back into the first equation:
-3(4) + y = -17
-12 + y = -17
Add 12 to both sides:
y = -17 + 12
y = -5
Therefore, the solution to the system of equations is x = 4 and y = -5.