Solve by whatever method you would prefer. (Leave answers as improper fractions)
3x + 2y = -10
2x – 5y = 3
Can someone give step by step?
Oh, solving equations, my favorite! Let's put on our mathematical clown shoes and tackle this.
Step 1: Let's start by eliminating one variable. I choose to eliminate the "x" variable. To do this, we need to make the coefficients of "x" in both equations the same. To make the coefficients of "x" the same, we can multiply the first equation by 2, and the second equation by 3. That will give us:
6x + 4y = -20
6x - 15y = 9
Step 2: Now we can subtract the second equation from the first equation to eliminate the "x" terms. So, we have:
(6x + 4y) - (6x - 15y) = -20 - 9
Simplifying this expression gives us:
6x + 4y - 6x + 15y = -29
The "x" terms cancel each other out, leaving us with:
19y = -29
Step 3: Now we can solve for "y" by dividing both sides of the equation by 19:
y = -29/19
So, the value of "y" is -29/19.
Step 4: Finally, we substitute the value of "y" back into one of the original equations to solve for "x". Let's pick the first equation:
3x + 2(-29/19) = -10
Simplifying this equation gives us:
3x - (58/19) = -10
To isolate the "x" term, we add (58/19) to both sides of the equation:
3x = -10 + (58/19)
Simplifying the right side of the equation gives us:
3x = (-190 + 58)/19
Further simplification gives us:
3x = -132/19
And finally, we divide both sides of the equation by 3:
x = (-132/19) / 3
Simplifying the right side of the equation gives us:
x = -132/57
So, the solution to the system of equations is x = -132/57 and y = -29/19.
Ta-da! We've solved the equations with a touch of clown magic.
To solve the system of equations:
3x + 2y = -10 ---(1)
2x - 5y = 3 ---(2)
We can use the method of substitution or elimination. I'll use the method of elimination.
Step 1: Multiply equation (1) by 5 and equation (2) by 2 to make the coefficients of y's equal and solve for y.
5(3x + 2y) = 5(-10)
2(2x - 5y) = 2(3)
Simplifying the above equations:
15x + 10y = -50
4x - 10y = 6
Adding equation (1) and equation (2) together to eliminate the term "-10y":
(15x + 10y) + (4x - 10y) = -50 + 6
Simplifying:
19x = -44
Step 2: Solve for x.
Divide both sides of the equation by 19:
1x = -44/19
So the value of x is -44/19.
Step 3: Substitute the value of x back into one of the original equations to solve for y.
Using equation (1):
3(-44/19) + 2y = -10
Simplifying:
-132/19 + 2y = -10
Adding 132/19 to both sides of the equation:
2y = -190/19 + 132/19
Simplifying:
2y = -58/19
Dividing both sides of the equation by 2:
y = -58/38
So the value of y is -58/38.
Therefore, the solution to the system of equations is x = -44/19 and y = -58/38.
To solve the system of equations:
1) We'll start by eliminating one variable by multiplying the equations by suitable constants so that the coefficients of either x or y are the same in both equations.
2) Let's eliminate the y variable first. Multiply the first equation by 5 and the second equation by 2 to make the coefficients of y the same, which will allow us to eliminate the y variable.
5(3x + 2y) = 5(-10)
2(2x - 5y) = 2(3)
Expanding the equations:
15x + 10y = -50
4x - 10y = 6
3) Add the two newly formed equations together to eliminate the y variable:
(15x + 10y) + (4x - 10y) = -50 + 6
Combining like terms:
19x = -44
4) Now, we'll solve for x by dividing both sides of the equation by 19:
x = -44/19
5) Substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
3(-44/19) + 2y = -10
Multiply:
-132/19 + 2y = -10
6) We want to isolate the y variable, so let's get rid of the fraction by multiplying through by 19 to clear the denominator:
19*(-132/19) + 19*(2y) = 19*(-10)
Simplifying:
-132 + 38y = -190
7) Solve for y by subtracting -132 from both sides:
38y = -190 + 132
38y = -58
8) Finally, divide both sides of the equation by 38:
y = -58/38
Simplifying the fractions is not necessary for this problem, so the final solution is:
x = -44/19
y = -58/38
I would choose elimination:
first one times 2 ---> 6x + 4y = -20
2nd times 3 -------> 6x - 15y = 9
subtract them:
19y = -29
y = -29/19
back into the original first:
3x - 58/19 = -10
3x = 58/19-10 = -132/19
x = -44/19