Multi-Step Equations
Systems of Equation
2x = y
4x - y = -2
please help!!!!!
I would use substitution
sub the 1st into the 2nd
4x - y = -2
4x - (2x) = -2
2x = -2
x = -1
then back into the first
y = 2x
y = 2(-1) = -2
thank you ....
2x + 4y = 24
x - 2y = -8
my mom tried helping me but didn't understand it....
For your second example I would use substitution again
Notice that in the second equation the x variable is all by itseld, that is, it is 1x understood.
That is the key.
look for a variable like that and solve for it
x - 2y = -8
x = 2y - 8
now sub that x value of (2y-8) into the other equation
2(2y-8) + 4y = 24
4y - 16 + 4y = 24
8y = 24 + 16
8y = 40
y = 40/8 = 5
now plug that into
x = 2y-8
x = 2(5)-8 = 2
so x=2, y=5
To solve this system of equations with two variables, we can use the method of substitution or elimination. I will explain both methods, so you can choose the one you find more comfortable.
Method 1: Substitution
Step 1: Begin with the first equation, which is 2x = y.
Step 2: Solve this equation for y to get y = 2x.
Step 3: Substitute the value of y in the second equation with 2x, since y = 2x.
Step 4: Rewrite the second equation with the substitution: 4x - (2x) = -2.
Step 5: Simplify the equation by combining like terms: 4x - 2x = -2.
Step 6: Solve for x: 2x = -2.
Step 7: Divide both sides of the equation by 2 to isolate x: x = -1.
Step 8: Now that we know x = -1, substitute this value back into the first equation to solve for y: y = 2(-1) = -2.
Therefore, the solution to the system of equations is x = -1 and y = -2.
Method 2: Elimination
Step 1: Begin with the two equations: 2x = y and 4x - y = -2.
Step 2: Multiply both sides of the first equation by -1 to create opposites: -2x = -y.
Step 3: Rewrite the second equation to align the signs of the y terms: 4x + y = -2.
Step 4: Now, add the two equations together, eliminating the y term: (-2x) + (4x) + (-y) + (y) = -2 + (-2).
Step 5: Simplify each side of the equation: 2x = -4.
Step 6: Divide both sides by 2 to solve for x: x = -2.
Step 7: Substitute the value of x back into the first equation to find y: 2(-2) = y, y = -4.
So, the solution to the system of equations is x = -2 and y = -4.