Solve this system of equations. 3x+y+60=180 5y-5+2x=180
3x+y+60=180 5y-5+2x=180
I would change the first one to
3x+y=120 and second one to
2x+5y=185
Multiply equation 1 by -5 and add to equation 2 to eliminate y. Solve for x.
To solve this system of equations, we will use a method known as substitution. Here's how we can proceed:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for y:
3x + y + 60 = 180
Subtract 3x and 60 from both sides:
y = 180 - 3x - 60
y = 120 - 3x
Step 2: Substitute the expression for y obtained in step 1 into the second equation.
Replace y in the second equation with 120 - 3x:
5(120 - 3x) - 5 + 2x = 180
Distribute 5 to the terms inside the parentheses:
600 - 15x - 5 + 2x = 180
Combine like terms:
-13x + 595 = 180
Subtract 595 from both sides of the equation:
-13x = -415
Divide both sides by -13:
x = 31.92 (rounded to two decimal places)
Step 3: Substitute the found value of x back into either of the original equations to solve for y.
Using the first equation:
3(31.92) + y + 60 = 180
95.76 + y + 60 = 180
155.76 + y = 180
Subtract 155.76 from both sides:
y = 24.24 (rounded to two decimal places)
Therefore, the solution to the system of equations is x ≈ 31.92 and y ≈ 24.24.