Solve for the following system of equAtions for y:
2x + y = 10
3x =y
2x + y = 10
3x =y
2x + 3x = 10
5x = 10
x = 2
Substitute 2 for x in the second equation.
To solve the system of equations for y, we'll use the method of substitution. Here are the steps:
Step 1: Start with the first equation: 2x + y = 10.
Step 2: Solve the second equation for y: 3x = y. Rearrange it to get y = 3x.
Step 3: Substitute the value of y from the second equation into the first equation. Replace y in the first equation with 3x:
2x + (3x) = 10.
Step 4: Simplify the equation by combining like terms:
5x = 10.
Step 5: Solve for x by dividing both sides of the equation by 5:
x = 10/5 = 2.
Step 6: Substitute the value of x into the second equation to find y:
y = 3x = 3(2) = 6.
Therefore, the solution to the system of equations is x = 2 and y = 6.
To solve this system of equations for y, we can eliminate one variable by substituting its value from one equation into the other equation. In this case, we can substitute the value of y from the second equation into the first equation.
Let's start by solving the second equation for y:
3x = y
Now, substitute this value of y in the first equation:
2x + 3x = 10
Combine like terms:
5x = 10
Divide both sides of the equation by 5:
x = 2
Now substitute the value of x back into one of the original equations to find the value of y. Let's use the second equation:
3(2) = y
Simplify:
6 = y
Therefore, the solution to the system of equations is:
x = 2
y = 6