Question

Help please ?! I need steps on how to do these..
1) Solve by substitution.
3x+y=-3
Y=x+5
2) How many solutions does the system of equations have?
Y=-x+8
Y=-x+7
3) How many solutions does the system of equations have?
2y=-2x+14
x+y=7
4) How many solutions does the system of equations have?
2y=-2x+14
x+3y=7

Answer 1

The substitution method of solving a system of equations works like this.
1. Solve one equation for one variable.
2. Substitute what that variable is equal to in the other equation.
3. Now you have an equation in one variable. Solve for that variable.
4. Substitute the known variable in one of the two original equations and solve for the other variable.

Answer 2

combine the two equations 3x + y = -3 and y = x + 5
first, put 3x + y = -3 into terms of y, making it y = -3x - 3
get rid of a variable by multiplying one (or both in a different case) equation by a value that will cancel out a variable, in this case, x. multiply y = x + 5 by 3, giving you y = 3x + 15.
then combine the equations in their new forms. since 3x + -3x = 0, y = 12.
go back to the original equations and substitute 12 for y.
3x + 12 = -3
12 = x + 5
combine.
y = -2x + 2
substitute.
12 = -2x + 2
x = -5
so the answer is -5, 12.
the answer is not wrong, but there is something wrong with the equation, as -5 does not work for y = x + 5...

Answer 3

@algebra1squared You have just explained the addition method. The problem specifically asks for the substitution method.