To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the two equations. Let's start by manipulating the first equation.
−2y = 10 − 5x
Multiply all terms by -3 to make the coefficients of y in both equations the same:
6y = -30 + 15x
Now the two equations are:
6y = -30 + 15x
−3y = −4x + 15
Next, we'll eliminate the y variable by adding the two equations together:
6y + (-3y) = -30 + 15x + (-4x) + 15
3y = 11x - 15
Divide by 3 to get y by itself:
y = (11/3)x - 5
Now that we have an equation for y in terms of x, we can substitute this into one of the original equations to solve for x. Let's substitute y = (11/3)x - 5 into the second equation:
−3((11/3)x - 5) = −4x + 15
-11x + 15 = -4x + 15
Subtract 15 from both sides:
-11x = -4x
Subtract -4x from both sides:
-7x=0
Divide by -7 to solve for x:
x=0
Now that we have found x=0, we can substitute this back into y = (11/3)x - 5 to solve for y:
y = (11/3)(0) - 5
y = -5
Therefore, the solution to the system of equations is x = 0 and y = -5.
A system of equations is given.
−2y = 10 − 5x
−3y = −4x +15
Solve for (x, y) using the elimination method. Show all work.
1 answer
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