Use the substitution method to solve each linear system:
-x+3y+1=0
3x-y+1=0
4x-3y=-13
-2x+y=4
Please help, thanks:):)!!!!
In #1, substitute x=3y+1 into 2nd equation
in #2, substitute y=2x+4 into the 1st equation
To solve the first linear system:
1. Start by solving one of the equations for one variable in terms of the other variable. Let's solve the first equation for x.
-x + 3y + 1 = 0
-x = -3y - 1
x = 3y + 1
2. Substitute this expression for x into the second equation.
3x - y + 1 = 0
3(3y + 1) - y + 1 = 0
9y + 3 - y + 1 = 0
8y + 4 = 0
8y = -4
y = -4/8
y = -1/2
3. Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation.
-x + 3(-1/2) + 1 = 0
-x - 3/2 + 1 = 0
-x - 3/2 + 2/2 = 0
-x - 1/2 = 0
-x = 1/2
x = -1/2
So, the solution to the first linear system is x = -1/2 and y = -1/2.
To solve the second linear system:
1. Start by solving one of the equations for one variable in terms of the other variable. Let's solve the second equation for y.
-2x + y = 4
y = 2x + 4
2. Substitute this expression for y into the first equation.
4x - 3(2x + 4) = -13
4x - 6x - 12 = -13
-2x - 12 = -13
-2x = -13 + 12
-2x = -1
x = -1/-2
x = 1/2
3. Substitute the value of x back into one of the original equations to solve for y. Let's use the second equation.
-2(1/2) + y = 4
-1 + y = 4
y = 4 + 1
y = 5
So, the solution to the second linear system is x = 1/2 and y = 5.