Find a solution to the following system of equations.
-5x + y = -5
-4x + 2y = 2
1st times -2
10x - 2y = 10
-4x + 2y = 2
add them
6x = 12
x = 2
into the 1st:
-10 + y = -5
y = 5
Why did the system of equations break up with each other? Because they had too many variables and not enough solutions!
To find a solution to the system of equations, we can use the method of substitution. We solve one equation for one variable and substitute that expression into the other equation.
Let's solve the first equation for y:
-5x + y = -5
y = 5x - 5
Now we substitute this expression for y in the second equation:
-4x + 2(5x - 5) = 2
Simplifying the equation:
-4x + 10x - 10 = 2
6x - 10 = 2
Adding 10 to both sides:
6x - 10 + 10 = 2 + 10
6x = 12
Dividing both sides by 6:
(6x)/6 = 12/6
x = 2
Now we substitute this value of x into the first equation to solve for y:
-5(2) + y = -5
-10 + y = -5
Adding 10 to both sides:
-10 + 10 + y = -5 + 10
y = 5
Therefore, the solution to the system of equations is x = 2 and y = 5.
To find a solution to the system of equations, we can use the method of substitution or elimination. Let's solve it using the method of elimination.
Given system of equations:
-5x + y = -5 ...(Equation 1)
-4x + 2y = 2 ...(Equation 2)
To eliminate one variable, we need to multiply one or both of the equations by constants so that the coefficients of one variable are the same in both equations. In this case, we can multiply Equation 1 by 2 to make the coefficient of y the same as in Equation 2.
Multiplying Equation 1 by 2:
2(-5x + y) = 2(-5)
-10x + 2y = -10 ...(Equation 3)
Now, we have Equation 3 and Equation 2 with the same coefficient for y. To eliminate y, we can subtract Equation 2 from Equation 3.
Subtracting Equation 2 from Equation 3:
(-10x + 2y) - (-4x + 2y) = (-10) - 2
-10x + 2y + 4x - 2y = -10 - 2
-6x = -12
Dividing both sides of the equation by -6, we get:
x = -12 / -6
x = 2
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use Equation 1.
Substituting x = 2 in Equation 1:
-5(2) + y = -5
-10 + y = -5
y = -5 + 10
y = 5
Therefore, the solution to the system of equations is x = 2 and y = 5.