solve the system of equations by elimination. 3x-4y=22 2x+5y=7

x=6

3x - 4y = 22

2x + 5y = 7

To eliminate variable x,
Multiply by -2 (3x - 4y = 22)
Multiply by 3 (2x + 5y = 7)

Add equations
-6x + 8y = -44
6x + 15y = 21
0 + 23y = -23
23y = -23
y = -1

To find x,
substitute y = -1, in 2x + 5y = 7
2x + 5y = 7
2x - 5 = 7
2x = 12
x = 6

x = 6, y = -1

3x+4y=-22

Your solving was helpful

To solve the system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. In this case, let's eliminate the "x" variable.

To eliminate the "x" variable, we need to manipulate the equations so that the coefficients of "x" in both equations are opposites of each other. We can do this by multiplying one or both of the equations by appropriate constants.

Let's start by multiplying the first equation by 2 and the second equation by 3. This will ensure that the coefficients of "x" in both equations will be opposites of each other.

2 * (3x - 4y) = 2 * 22 -> 6x - 8y = 44
3 * (2x + 5y) = 3 * 7 -> 6x + 15y = 21

Now, we have two equations:

6x - 8y = 44
6x + 15y = 21

Next, we'll subtract one equation from the other to eliminate the "x" variable.

(6x - 8y) - (6x + 15y) = 44 - 21

Simplifying:

6x - 8y - 6x - 15y = 23

Combining like terms:

-23y = 23

Dividing both sides by -23:

y = -1

Now that we have the value of "y", we can substitute it back into either of the original equations to find the value of "x". Let's substitute it into the first equation:

3x - 4(-1) = 22

Simplifying:

3x + 4 = 22

Subtracting 4 from both sides:

3x = 18

Dividing both sides by 3:

x = 6

So, the solution to the system of equations is x = 6 and y = -1.