Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-3x + y = 4
x + 3y = 22
Here's what I came up with (where did I go wrong)
-3x + y = 4
y = 4 - 3x
-3x + (4-3x) = 4
-3x + 1x = 4
-2x = 4
x= -2
-2x + 3(4 - 3x) = 22
-2x + 12 -9x = 22
-2x + 3x = 22
1x = 22
x = 21
when you are using APE or addition property of inequality you should also change the sign of it. this is the part where you got wrong.-3x+y=4 it should be y=4+3x and not y=4-3x. notice the sign of your 3x. always remember that when you transfer a term its sign show be revised
malay ko sau bhala ka!!!
To use the substitution method, you correctly isolated 'y' in the first equation: y = 4 - 3x. However, you made an error when substituting this value into the second equation.
Let me walk you through the correct steps:
Start with the system of equations:
-3x + y = 4 [equation 1]
x + 3y = 22 [equation 2]
We can solve the first equation for 'y':
y = 4 - 3x [equation 1 rewritten]
Now substitute this expression for 'y' into the second equation:
x + 3(4 - 3x) = 22
Distribute the 3:
x + 12 - 9x = 22
Combine like terms:
-8x + 12 = 22
Subtract 12 from both sides:
-8x = 10
Divide by -8:
x = -10/8
Simplify:
x = -5/4
Now substitute the value of 'x' back into equation 1 to solve for 'y':
-3(-5/4) + y = 4
Multiply -3 by -5/4:
15/4 + y = 4
Subtract 15/4 from both sides:
y = 4 - 15/4
Find a common denominator and simplify:
y = (16 - 15)/4
y = 1/4
Therefore, the solution to the system of equations is:
x = -5/4
y = 1/4
So, it seems like your mistake occurred when you substituted the value of 'x' into the second equation. Make sure to fully distribute the coefficient (3) to all terms inside the parentheses.