i need help solving the system by addition.
5x-7y=5
x+3y=1
this is what i think but i am not sure
3y=-x+1
y= -(1/3)x+(1/3)
5x - 7 (-1/3x + 1/3) = 5
5x+2.3333331x-2.3333331=5
7.3333331x-2.3333331=5
7.3333331x=7.3333331
x=1
x+3y=1
1+3y=1
3y=1-1
3y=0
y=0
so my solutions i get is
x = 1 and y = 0
You have the solution ,but you did not get it by addition.
5x-7y=5
x+3y=1
Multiply the second equation by -5
5x-7y=5
-5x-15y=-5
Now add the equations.
0x - 22y= 0
solve, y=0
5x-7y=5
x+3y=1
Put y=0 into either equation, and solve for x.
{5x-3y=11
{3x+y=1
To solve the system by addition, you can choose to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable x by multiplying the second equation by 5 and adding it to the first equation:
5x - 7y = 5
x + 3y = 1
Multiply the second equation by 5:
5(x + 3y) = 5(1)
5x + 15y = 5
Now, add the two equations together:
(5x - 7y) + (5x + 15y) = 5 + 5
10x + 8y = 10
Simplify the equation:
10x + 8y = 10
To solve for one variable, you can isolate it by subtracting or adding the equations together. In this case, subtract the first equation from the second equation:
(10x + 8y) - (5x - 7y) = 10 - 5
10x + 8y - 5x + 7y = 5
Simplify the equation:
5x + 15y = 5
Now, we have a new equation:
5x + 15y = 5
To eliminate the variable x, we can subtract this new equation from the original equation we obtained when we added the two original equations:
(10x + 8y) - (5x + 15y) = 10 - 5
10x + 8y - 5x - 15y = 5
Simplify the equation:
5x - 7y = 5
Now, we have a new equation:
5x - 7y = 5
Comparing this new equation to the first equation we obtained when adding the original equations, we can see that they are the same equation:
5x - 7y = 5
5x - 7y = 5
This means that the system of equations is dependent or consistent, and there are infinite solutions. The variables x and y can take on any real values that satisfy the equation.
Therefore, you are correct in your solution:
x = 1 and y = 0