5x-4y= -3
2x + 7y= 5
How to solve this linear system shown above by using elimination strategy ?
(5x-4y= -3) *2 ->10x - 12y= 6
(2x + 7y= 5) *5 -> 10 +35y= 25
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-47y = -19
y = -19/47
10x - 12y= 6
10x - 12(0.4) = 6
10x -4.8=6
x=1.08
I seem to get the final answer wrong. correct me if Im wrong overtime i verify. THanks
You're doing the elimination method right. :) But there's just some errors in multiplying. In your first equation (5x - 4y = -3), you multiplied it by 2.
5x * 2 = 10x, yes that's right.
-4y * 2 = -8y, not -12y as you've typed.
-3 * 2 = -6, not 6 as you've typed.
oh sorry, I know I type it in wrong number. But even I tries in correct number. I still didn't get it right?
Why is that? Anyway, let's solve for y. I'll multiply the first equation by -2 instead of 2:
(5x - 4y = -3) * -2 ---> -10x + 8y = 6
(2x + 7y = 5) * 5 ---> 10x + 35y = 25
Add them together:
-10x + 8y = 6
10x + 35y = 25
----------------------
43y = 31
y = 31/43
Now that you have a value for y, substitute this to either equation to get x. Let just choose the first equation:
5x - 4y = -3
5x - 4(31/43) = -3
x = ?
hope this helps~ `u`
To solve the given linear system using the elimination strategy, you need to eliminate one variable by multiplying one or both equations by a suitable number(s) so that when you add or subtract the equations together, one variable cancels out.
Let's go through the steps again:
1. Given equations:
5x - 4y = -3 --- Equation 1
2x + 7y = 5 --- Equation 2
2. Multiply Equation 1 by 2 and Equation 2 by 5 to make the coefficients of x in both equations the same:
2 * (5x - 4y) = 2 * (-3) ---> 10x - 8y = -6 --- Equation 3
5 * (2x + 7y) = 5 * 5 ---> 10x + 35y = 25 --- Equation 4
Now, the coefficients of x in both Equation 3 and Equation 4 are the same (10x), so we can subtract Equation 3 from Equation 4 to eliminate x.
3. Subtract Equation 3 from Equation 4:
(10x + 35y) - (10x - 8y) = 25 - (-6)
10x + 35y - 10x + 8y = 25 + 6
43y = 31
4. Solve for y:
Divide both sides by 43:
y = 31 / 43
y ≈ 0.7209 (rounded to four decimal places)
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.
5. Substitute y = 0.7209 into Equation 1:
5x - 4(0.7209) = -3
5x - 2.8836 = -3
5x = -3 + 2.8836
5x = -0.1164
6. Solve for x:
Divide both sides by 5:
x = -0.1164 / 5
x ≈ -0.0233 (rounded to four decimal places)
The solution to the linear system is approximately x ≈ -0.0233 and y ≈ 0.7209.
Please double-check your calculations to make sure you have the correct answer.