Use the substitution method to solve
-x + 3y=24
5x +8y=-5
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To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
-x + 3y = 24
Adding x to both sides:
3y = x + 24
Dividing both sides by 3:
y = (1/3)x + 8
Step 2: Substitute the expression you found for y into the other equation.
Substituting y = (1/3)x + 8 into the second equation:
5x + 8((1/3)x + 8) = -5
Step 3: Simplify and solve for the remaining variable.
Expanding and simplifying the equation:
5x + (8/3)x + 64 = -5
Multiplying all terms by 3 to clear the fraction:
15x + 8x + 192 = -15
Combining like terms:
23x + 192 = -15
Subtracting 192 from both sides:
23x = -207
Dividing both sides by 23:
x = -9
Step 4: Substitute the value found for x back into one of the original equations to solve for y.
Using the first equation, substituting x = -9:
-(-9) + 3y = 24
9 + 3y = 24
Subtracting 9 from both sides:
3y = 15
Dividing both sides by 3:
y = 5
Therefore, the solution to the system of equations is x = -9 and y = 5.
Manipulating the first equation, we get:
x = 3y - 24
5x + 8y = -5
Substitute 3y-24 for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.