Can you check these thanks.
Solve the system by substitution or elimination.
2x+y=1
3x-y=14
Answer: (3,5)
x-3y= -12
2x + 11y= -7
Answer: (39,17)
4x+2y=8
12x+6y=24
Answer: no solution
4x-2y=5
2x-y= -1
Answer: no solution
4a+3b =6
8a-b= -9
Answer: no solution
2x+y=1
3x-y=14
Answer: (3,5)
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Hey, you can check easily. Just put the values in for x and y
2(3)+5 = 8 not 1 - NO WAY
on the last
4a+3b=6
24a-3b=-27 ( I multiplied by 3), then add
28a=-19
why did you get no solution?
others are correct.
First one should be (3,-5)
To solve these systems of equations, we can use the methods of substitution or elimination. Let's go through each system one by one:
1. System:
2x + y = 1
3x - y = 14
To solve this system by substitution, we'll start by isolating one variable in either of the equations. Let's isolate y in the first equation:
y = 1 - 2x
Now we can substitute this expression for y into the second equation:
3x - (1 - 2x) = 14
Simplifying this equation, we get:
3x - 1 + 2x = 14
5x - 1 = 14
5x = 15
x = 3
Now that we have the value of x, we can substitute it back into either of the original equations to find y:
2(3) + y = 1
6 + y = 1
y = -5
So the solution to the system is (x, y) = (3, -5).
2. System:
x - 3y = -12
2x + 11y = -7
Let's solve this system using the method of elimination. We'll multiply the first equation by 2 and the second equation by 3 to make the coefficients of x equal:
2x - 6y = -24
6x + 33y = -21
Next, we'll subtract the first equation from the second equation to eliminate x:
(6x + 33y) - (2x - 6y) = (-21) - (-24)
4x + 39y = 3
Now we have a new equation with only variables y and x. Let's isolate x by subtracting 39y from both sides:
4x = 3 - 39y
x = (3 - 39y)/4
Now we can substitute this expression for x back into either of the original equations to solve for y. For simplicity, let's use the first equation:
(3 - 39y)/4 - 3y = -12
Simplifying this equation, we get:
3 - 39y - 12y = -48
-51y = -51
y = 1
Substituting this value of y back into the first equation:
x - 3(1) = -12
x - 3 = -12
x = -9
So the solution to this system is (x, y) = (-9, 1).
The remaining systems cannot be solved as they have inconsistent equations which contradict each other. Therefore, the answers are "no solution" for those systems.