9X+y=2
-4X-y=17
use elimination method to solve it.
9 x + y = 2
-4 x- y = 17 Add
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9 x + ( - 4x ) + y + ( - y ) = 2 + 17
9 x - 4 x + y - y = 2 + 17
5 x + 0 = 19
5 x = 19 Divide both sides by 5
x = 19 / 5 = 3.8
9 x + y = 2
9 * 19 / 5 + y = 2
171 / 5 + y = 2
y = 2 - 171 / 5
y = 10 / 5 - 171 / 5
y = - 161 / 5
y = - 32.2
To solve the system of equations:
1. First, let's use the second equation to solve for y.
Rearrange the equation: -4X - y = 17
Add 4X to both sides: -y = 4X + 17
Multiply both sides by -1: y = -4X - 17
2. Now we have the value of y in terms of X. Next, substitute this value of y into the first equation.
Replace y in the equation 9X + y = 2: 9X + (-4X - 17) = 2
Simplify the equation: 9X - 4X - 17 = 2
Combine like terms: 5X - 17 = 2
3. Next, isolate X by adding 17 to both sides of the equation: 5X = 2 + 17
Simplify: 5X = 19
4. Finally, solve for X by dividing both sides of the equation by 5: X = 19/5
Thus, X = 19/5.
To find the value of y, substitute this value of X back into one of the original equations. Let's use the first equation:
9X + y = 2
Substitute X = 19/5: 9(19/5) + y = 2
Multiply: (171/5) + y = 2
Subtract (171/5) from both sides: y = 2 - (171/5)
Simplify: y = (10 - 171)/5
y = -161/5.
Therefore, the solution to the system of equations is X = 19/5 and y = -161/5.