How o Isolve by using the elimination method.
5x + 5y= -7
7x - 2y= 17
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Elimination involves multiplying one or more equations to either eliminate the x's or y's.
Multiplying the top equation by 2 and the bottom equation by 5 will eliminate the y's.
10x+10y=-14
35x-10y=85
Now add the equations together.
45x=71
Divide both sides by 45 to solve by x.
x=?
Now plug that number into any of the equations to figure out what y is. Post your answer if you'd like it checked.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Choose one of the equations and multiply it by a constant so that the coefficients of one of the variables (either x or y) in both equations will be the same when added or subtracted together. In this case, we can choose to make the coefficient of y the same in both equations.
Let's multiply the first equation by 2 and the second equation by 5 to eliminate y.
2(5x + 5y) = 2(-7)
5(7x - 2y) = 5(17)
Simplifying these equations will give you:
10x + 10y = -14
35x - 10y = 85
Step 2: Add the two equations together or subtract one from the other to eliminate one variable.
(10x + 10y) + (35x - 10y) = -14 + 85
Simplifying this equation will give you:
45x = 71
Step 3: Solve for x by dividing both sides of the equation by the coefficient of x.
x = 71 / 45
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation.
5(71 / 45) + 5y = -7
Simplifying this equation will give you:
71/9 + 5y = -7
Step 5: Solve for y by isolating y on one side of the equation.
5y = -7 - 71/9
5y = -63/9 - 71/9
5y = -134/9
Dividing both sides by 5 will give you:
y = -134/45
Therefore, the solution to the system of equations is x = 71/45 and y = -134/45.