Which of the following would be the best first step when solving the following system using the substitution method?
• x - y = -4 ;
• x + 2y = 5
x = -4 - y
x = -4 + y
2y = 5 - x
2y = 5 + x
I have solved the equation but I am unsure which is the best first step.
x-y=-4
x+2y=5
y=x+4
x+2y=5
x+2(x+4)=5
x=-1
y=x+4
y=-1+4
y=3
Could you please tell me which is the best first step?
If you insist on using substitution the logical first step is
x = -4 + y
then
-4 + y + 2 y = 5
3 y = 9
y = 3
To solve this system using the substitution method, the best first step would be to isolate one variable in one of the equations and then substitute it into the other equation.
In this case, let's isolate "x" in the first equation (x - y = -4):
1. Add "y" to both sides of the equation to isolate "x":
x = -4 + y
Now, substitute this value for "x" into the second equation (x + 2y = 5):
2. Replace "x" with the value (-4 + y) in the second equation:
(-4 + y) + 2y = 5
Simplify the equation by combining like terms:
3. -4 + y + 2y = 5
-4 + 3y = 5
Next, solve for "y" by isolating it on one side of the equation:
4. Add 4 to both sides to isolate 3y:
-4 + 4 + 3y = 5 + 4
3y = 9
Divide both sides by 3 to solve for "y":
5. (3y)/3 = 9/3
y = 3
Now that we have the value for "y", substitute it back into one of the original equations to solve for "x". Let's use the first equation (x - y = -4):
6. Substitute y = 3 into the first equation:
x - 3 = -4
Isolate "x" by adding 3 to both sides:
7. x - 3 + 3 = -4 + 3
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 3.