x+3y = 10 & x=2y-5
could someone explain how to do this.
x+3y = 10
x=2y-5
Substitute.
x = 10 - 3y
10 - 3y = 2y - 5
15 = 5y
3 = y
x + 3y = 10
x + 3(3) = 10
x = 1
ohh, thank you!
You are very welcome.
To solve this system of equations, you can use the substitution method or the elimination method. Let's use the substitution method.
First, we'll solve one equation for one variable and then substitute that expression into the other equation.
Given:
Equation 1: x + 3y = 10
Equation 2: x = 2y - 5
Step 1: Solve Equation 2 for x:
x = 2y - 5
Step 2: Substitute this expression for x in Equation 1:
(2y - 5) + 3y = 10
Now, let's simplify and solve for y:
2y - 5 + 3y = 10
5y - 5 = 10
5y = 10 + 5
5y = 15
y = 15/5
y = 3
Step 3: Substitute the value of y back into Equation 2 to find x:
x = 2(3) - 5
x = 6 - 5
x = 1
So the solution to the system of equations is x = 1 and y = 3.
You can also check the solution by substituting the values of x and y back into both original equations to ensure they satisfy the equations.