[[-3x+2y=10],[-4x+3y=2]]
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.
Step 1: Multiply the first equation by 4 and the second equation by 3 to eliminate the x terms.
-12x + 8y = 40
-12x + 9y = 6
Step 2: Subtract the second equation from the first equation.
-12x + 8y - (-12x + 9y) = 40 - 6
-12x + 8y + 12x - 9y = 34
- y = 34
Step 3: Solve for y.
y = -34
Step 4: Substitute the value of y back into either of the original equations to solve for x.
-3x + 2(-34) = 10
-3x - 68 = 10
-3x = 78
x = -26
So the solution to the system of equations is x = -26 and y = -34.
The given system of equations is:
-3x + 2y = 10 ...(1)
-4x + 3y = 2 ...(2)
To solve this system of equations, we can use the method of elimination or substitution. I will explain both methods, and then you can choose which one you want to use.
Method 1: Elimination
Step 1: Multiply both sides of equation (1) by 4 and equation (2) by 3 to make the coefficients of x in both equations the same (12 and -12, respectively).
(4)(-3x + 2y) = (4)(10)
(3)(-4x + 3y) = (3)(2)
-12x + 8y = 40 ...(3)
-12x + 9y = 6 ...(4)
Step 2: Now, subtract equation (4) from equation (3) to eliminate x.
(-12x + 8y) - (-12x + 9y) = 40 - 6
-12x + 8y + 12x - 9y = 34
-y = 34
Step 3: Rearrange the equation to solve for y.
y = -34
Step 4: Substitute the value of y into either equation (1) or (2) to find the value of x.
Using equation (1):
-3x + 2(-34) = 10
-3x - 68 = 10
-3x = 10 + 68
-3x = 78
x = -78/3
x = -26
Therefore, the solution to the system of equations is x = -26 and y = -34.
Method 2: Substitution
Step 1: Solve one equation for one variable in terms of the other variable and substitute it into the other equation.
From equation (1), solve for x:
-3x = -2y + 10
x = (2y - 10)/3
Step 2: Substitute this expression for x in equation (2).
-4((2y - 10)/3) + 3y = 2
Simplify the equation by multiplying through by 3 to get rid of the fraction:
-4(2y - 10) + 9y = 6
Step 3: Solve for y.
-8y + 40 + 9y = 6
y + 40 = 6
y = -34
Step 4: Substitute the value of y back into the expression for x.
x = (2(-34) - 10)/3
x = -26
Again, we get the solution x = -26 and y = -34.
And that's how you solve the given system of equations.
To solve the system of equations:
1. Let's start by multiplying the first equation by 3 and the second equation by 2 to eliminate the y terms.
- Equation 1: -9x + 6y = 30
- Equation 2: -8x + 6y = 4
2. Now, subtract Equation 2 from Equation 1 to eliminate the y terms:
- (-9x + 6y) - (-8x + 6y) = 30 - 4
- -9x + 6y + 8x - 6y = 26
- -x = 26
3. Simplify Equation -1x = 26 and solve for x:
- Divide both sides of the equation by -1: x = -26
4. Now substitute the value of x into one of the original equations. Let's use the first equation:
- -3(-26) + 2y = 10
- 78 + 2y = 10
5. Solve for y:
- Add 78 to both sides of the equation: 2y = 10 - 78
- 2y = -68
6. Divide by 2 on both sides of the equation to solve for y:
- y = -34
So, the solution to the system of equations is x = -26 and y = -34.