Solving Systems by Substitution:
2. x=1-4y
2x+7y=3
I need help learning how to do this problem step-by-step
your first equation says that
x = 1-4y
so "substitute" 1-4y wherever you see x in the other equation
2x+7y=3
2(1-4y) + 7y = 3
2 - 8y + 7y = 3
-y = 1
y = -1
next sub that y = -1 back into the first equation
x = 1 - 4(-1) = 1+4 = 5
x = 1-4y
2x+7y=3
Starting with the first equation
since x = 1 - 4y
Plug that in to the second equation
2(1-4y)+7y=3
2 -8y + 7y = 3
2 - y = 3
2/2 - y = 3/2
- y = 3/2
Since why can't be negative, move the negative over to the other side
y = -3/2
Okay we found what Y is now plug that into the first equation
x = 1-4(-3/2)
x = 1 + 6
x = 7
so the answer is (7,-3/2)
I'm pretty sure this is right, but I hope a real tutor comes and say for sure
Oh sorry, I did my math wrong and Divided instead of subtracting.
To solve this system of equations using the method of substitution, follow these step-by-step instructions:
Step 1: Start with the first equation, which is x = 1 - 4y.
Step 2: Substitute the value of x from the first equation into the second equation. Replace x with (1 - 4y) in the equation 2x + 7y = 3.
2(1 - 4y) + 7y = 3
Simplify this equation:
2 - 8y + 7y = 3
Combine like terms:
2 - y = 3
Step 3: Solve the equation you obtained in step 2 to find the value of y. Subtract 2 from both sides:
-y = 3 - 2
Simplify:
-y = 1
To isolate y, multiply both sides of the equation by -1:
y = -1
Step 4: Substitute the value of y back into the first equation (x = 1 - 4y) or the second equation (2x + 7y = 3) to find the value of x. Let's use the first equation.
x = 1 - 4(-1)
x = 1 + 4
x = 5
Therefore, the solution to the system of equations is x = 5 and y = -1.