Solve the system by substitution.
10, x, plus, 5, y, equals, minus, 50
10x+5y=
−50
y, equals, minus, x
y=
−x
Substituting −x for y in the first equation, we get:
10x + 5(−x) = −50
Simplifying,
10x − 5x = −50
5x = −50
Dividing both sides by 5,
x = −10
Now, substituting x = −10 in the equation y = −x, we find:
y = −(−10)
y = 10
Therefore, the solution to the system of equations is x = −10 and y = 10.
To solve the system by substitution, we can substitute the second equation into the first equation.
Substituting y = -x into the first equation:
10x + 5y = -50
10x + 5(-x) = -50
10x - 5x = -50
5x = -50
Divide both sides of the equation by 5:
5x/5 = -50/5
x = -10
Now that we found the value of x, we can substitute it back into the second equation to solve for y:
y = -x
y = -(-10)
y = 10
Therefore, the solution to the system is x = -10 and y = 10.
To solve the system by substitution, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable. In this case, we have the equation: y = -x.
2. Substitute the expression you found for y in the other equation. The other equation is: 10x + 5y = -50. Replace y with -x in this equation to get: 10x + 5(-x) = -50.
3. Solve the resulting equation for x. Distribute 5 to -x: 10x - 5x = -50. Combine like terms: 5x = -50.
4. Solve for x by dividing both sides of the equation by 5: x = -10.
5. Once you have the value for x, substitute it back into one of the original equations to solve for y. Using y = -x, substitute -10 for x: y = -(-10). Simplify: y = 10.
Therefore, the solution to the system of equations is x = -10 and y = 10.