Determine the solution of the following systems of linear equations using elimination.
2x + 3y = 7
x – 2y – 4 = 0
rearrange things a bit to get
2x + 3y = 7
x - 2y = 4
Now double the 2nd equation and you have
2x + 3y = 7
2x - 4y = 8
Now subtract and you have
7y = -1
And your way is clear...
that isn't correct because you cannot do 7y/7=-1/7 to get a whole number for y.
so, who said y is an integer?
To solve the system of linear equations using elimination, we can eliminate one of the variables by multiplying one or both equations by suitable constants. Here's how to do it step by step:
1. Look at the two equations given:
2x + 3y = 7 ...(Equation 1)
x – 2y – 4 = 0 ...(Equation 2)
2. To eliminate one variable, we need to choose a coefficient that can be made the same for either the x or y term in both equations. In this case, we can see that the coefficient of x in Equation 2 is 1, which can be easily manipulated.
3. Multiply Equation 2 by 2 to make the coefficient of x the same:
2(x – 2y – 4) = 0
2x – 4y – 8 = 0 ...(Equation 3)
4. Now, we have two equations with the same coefficient of x:
2x + 3y = 7 ...(Equation 1)
2x – 4y – 8 = 0 ...(Equation 3)
5. Subtract Equation 3 from Equation 1 to eliminate x:
(2x + 3y) - (2x – 4y) = (7) - (–8)
2x + 3y - 2x + 4y = 7 + 8
7y = 15
6. Solve for y by dividing both sides of the equation by 7:
(7y)/7 = 15/7
y = 15/7
7. Substitute the value of y back into either Equation 1 or Equation 2 to find the value of x. Let's substitute it into Equation 1:
2x + 3(15/7) = 7
2x + 45/7 = 7
8. Multiply through by 7 to get rid of the fraction:
7(2x) + 7(45/7) = 7(7)
14x + 45 = 49
9. Subtract 45 from both sides of the equation:
14x = 49 - 45
14x = 4
10. Solve for x by dividing both sides of the equation by 14:
(14x)/14 = 4/14
x = 4/14
11. Simplify the fraction:
x = 2/7
So, the solution to the system of linear equations is x = 2/7 and y = 15/7.