Solve simultaneously: x -2y = 4, 2x + 5y = 17
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To solve the system of equations:
x - 2y = 4
2x + 5y = 17
There are several ways to solve this system, such as substitution, elimination, or using matrices. In this case, we'll use the method of elimination.
Step 1: Multiply the first equation by 2, so that the coefficients of x in both equations are the same. This will allow us to cancel out the x term when we add the equations together.
2(x - 2y) = 2(4)
2x - 4y = 8
Now, we have two equations with the same coefficient for x:
2x - 4y = 8
2x + 5y = 17
Step 2: Add the two equations together to eliminate the x term.
(2x - 4y) + (2x + 5y) = 8 + 17
4x + y = 25
Step 3: Solve the resulting equation for y.
4x + y = 25
Subtract 4x from both sides:
y = 25 - 4x
Step 4: Substitute the value of y in terms of x into one of the original equations. Let's use the first equation.
x - 2(25 - 4x) = 4
x - 50 + 8x = 4
9x - 50 = 4
Step 5: Solve for x.
Add 50 to both sides:
9x = 54
Divide by 9:
x = 6
Step 6: Substitute the value of x into one of the original equations to solve for y. Using the first equation:
6 - 2y = 4
Subtract 6 from both sides:
-2y = -2
Divide by -2:
y = 1
Therefore, the solution to the system of equations is x = 6 and y = 1.
since x = 2y+4,
2(2y+4)+5y = 17
y = 1
so x = 2y+4 = 6