x+y=5
x-3y=3
I am not sure what you are aiming for. Mainly because you have not stated if this is an "and" , "or" equation.
Hope this helps.
Problem:
Solve x+y=5;x−3y=3
Steps:
I will try to solve your system of equations.
x+y=5;x−3y=3
Step: Solve x+y=5 for x:
x+y+−y=5+−y(Add -y to both sides)
x=−y+5
Step: Substitute (−y+5) for x in x−3y=3:
x−3y=3
−y+5−3y=3
−4y+5=3(Simplify both sides of the equation)
−4y+5+−5=3+−5(Add -5 to both sides)
−4y=−2
−4y
−4
=
−2
−4
(Divide both sides by -4)
y=
1
2
Step: Substitute (
1
2
) for y in x=−y+5:
x=−y+5
x=−
1
2
+5
x=
9
2
(Simplify both sides of the equation)
Answer:
x=9/2
and y= 1/2
a little less work would be to note that if you subtract one equation from the other, the x's disappear:
x+y=5
x-3y=3
4y = 2
y = 1/2
Then use that value of y in either equation to get x.
To solve this system of equations, we can use the method of substitution or elimination. I will explain both methods, and you can choose which one you prefer.
Method 1: Substitution
1. Solve one equation for one variable in terms of the other variable.
Let's solve the first equation, x + y = 5, for x:
x = 5 - y
2. Substitute the expression for x into the second equation.
Instead of writing x in the second equation, we can write (5 - y), which gives us:
(5 - y) - 3y = 3
3. Simplify and solve for y.
5 - y - 3y = 3
5 - 4y = 3
-4y = 3 - 5
-4y = -2
y = (-2) / (-4)
y = 1/2
4. Substitute the value of y back into one of the original equations to solve for x.
Let's use the first equation, x + y = 5:
x + 1/2 = 5
x = 5 - 1/2
x = 9/2 or 4.5
So, the solution to the system of equations is x = 4.5 and y = 0.5.
Method 2: Elimination
1. Multiply one or both equations by a constant to make the coefficients of one variable in both equations the same or opposite.
In this case, we can multiply the second equation by 1, and the coefficients of y will become -3 in both equations.
2. Add or subtract the two equations to eliminate one variable.
(x + y) + (x - 3y) = 5 + 3
x + y + x - 3y = 8
2x - 2y = 8
3. Simplify and solve for x or y.
2x - 2y = 8
2(x - y) = 8
x - y = 4
4. Solve for one variable in terms of the other.
x = y + 4
5. Substitute this expression for x into one of the original equations to solve for the remaining variable.
Let's use the first equation, x + y = 5:
(y + 4) + y = 5
2y + 4 = 5
2y = 5 - 4
2y = 1
y = 1/2
6. Substitute the value of y back into the expression for x to find its value.
x = (1/2) + 4
x = (1/2) + (8/2)
x = 9/2 or 4.5
So, the solution to the system of equations is x = 4.5 and y = 0.5.
You can choose either the substitution method or the elimination method to solve systems of equations depending on your preference and the specific problem at hand.