solving with elimination 7x-4y=13 2x-5y =-4
14 x - 8 y = 26
14 x - 35y = -28
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27 y = 54
y = 2
2 x = -4 + 5(2)
x = -2 + 5
x = 3
To solve the system of equations using the elimination method, we want to eliminate one of the variables by manipulating the equations so that when we add or subtract them, one of the variables cancels out. In this case, we can eliminate the x variable by manipulating the equations.
Let's start by multiplying both sides of the second equation by 7 and the first equation by 2, which will give us:
14x - 8y = 26
14x - 35y = -28
Now, let's subtract the second equation from the first equation to eliminate the x variable:
(14x - 8y) - (14x - 35y) = 26 - (-28)
Simplifying this equation will give us:
14x - 8y - 14x + 35y = 26 + 28
The 14x terms will cancel out, and we are left with:
-8y + 35y = 54
Combining like terms gives us:
27y = 54
Dividing both sides of the equation by 27 will give us:
y = 54/27
Simplifying that further gives us:
y = 2
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
7x - 4(2) = 13
Simplifying this equation gives us:
7x - 8 = 13
Adding 8 to both sides of the equation gives us:
7x = 21
Dividing both sides of the equation by 7 gives us:
x = 21/7
Simplifying that further gives us:
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 2.