x=-2y+1
x+3y=-2
Please help me solve each system of equations and show your work thanks.
(-2y+1) + 3 y = -2
y + 1 = -2
y = -3
x = -2(-3) + 1
x = 7
perfectly set up for using substitution
sub the 1st into the 2nd
x + 3y = -2
(-2y+1) + 3y = -2
-2y + 1 + 3y + -2
y = -3
back into the 1st: x = -2(-3)+1 = 7
x = 7 , y = -3
2y/3+27+3y/4=-24
To solve this system of equations, we can use either substitution or elimination method. Let's use the elimination method.
1. Multiply the first equation by 3:
3x = -6y + 3
2. Keep the second equation as it is:
x + 3y = -2
Now, we can eliminate x by adding the two equations together:
3x + x = (-6y + 3) + (x + 3y)
4x = -6y + x + 3 + 3y
Combine like terms:
4x = -3y + 3
Now, let's solve for y by isolating it:
4x + 3y = 3
Subtract 4x from both sides:
3y = -4x + 3
Divide both sides by 3:
y = (-4/3)x + 1
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
x = -2y + 1
Substitute y = (-4/3)x + 1:
x = -2((-4/3)x + 1) + 1
Simplify the expression:
x = (8/3)x - 2 + 1
x = (8/3)x - 1
Move the (8/3)x term to the left side:
x - (8/3)x = -1
Combine the x terms:
(3/3)x - (8/3)x = -1
(-5/3)x = -1
Multiply both sides by -3/5 to get x by itself:
x = (-1) * (-3/5)
x = 3/5
Therefore, the solution to the given system of equations is x = 3/5 and y = (-4/3)(3/5) + 1 = -4/5 + 1 = 1/5.
Note that substitution method is another way to solve the system of equations, but the steps may vary slightly.