6x-4y=54

-9x+2y=-69

Which system would work best to solve?

Please show work and solve. (all steps)

Thank You

I honestly don't know how to do this.

I would use elimination, where we attempt to get the coefficients of either x or y to be the same or to be opposite

1st equation --> 6x - 4y = 54
2nd times 2 --> -18x + 4y = -138
add them:
-12x = -84
divide by -12
x = 7

sub back into the first
6(7) - 4y = 54
-4y = 12
y = -3

x = 7, y = -3

sub those values into both equations to verify that my answer is correct (it works !)

Thank you very much....

x + 4y = 54

No worries! I'll be happy to help you solve this system of equations step by step.

To determine which method would work best, let's take a look at the coefficients of the variables (x and y) in each equation.

In the first equation, we have:
6x - 4y = 54

In the second equation, we have:
-9x + 2y = -69

Notice that the coefficients in both equations are not easily eliminated by multiplying one or both equations by a constant. Therefore, the most efficient method to solve this system is by using the method of elimination.

Here are the steps to solve this system:

Step 1: Multiply both sides of the second equation by 3. This helps to make the coefficients of x in both equations match in absolute value.
-9x + 2y = -69 becomes:
-27x + 6y = -207

Now, our system is:
6x - 4y = 54
-27x + 6y = -207

Step 2: Add the two equations together. This will eliminate the variable y.
(6x - 4y) + (-27x + 6y) = 54 + (-207)
Simplifying the left side and the right side:
-21x + 2y = -153

Step 3: Now, let's work on eliminating the variable y. Multiply the first equation by 3.
3(6x - 4y) = 3(54)
18x - 12y = 162

Our system becomes:
18x - 12y = 162
-21x + 2y = -153

Step 4: Add the two equations together. This will eliminate the variable y.
(18x - 12y) + (-21x + 2y) = 162 + (-153)
Simplifying the left side and the right side:
-3x = 9

Step 5: Solve for x by dividing both sides of the equation by -3.
-3x / -3 = 9 / -3
x = -3

Step 6: Substitute the value of x into either of the original equations to find the value of y. Let's use the first equation:
6x - 4y = 54
6(-3) - 4y = 54
-18 - 4y = 54

Step 7: Simplify the equation:
-4y = 54 + 18
-4y = 72

Step 8: Solve for y by dividing both sides of the equation by -4.
-4y / -4 = 72 / -4
y = -18

Therefore, the solution to the system of equations is x = -3 and y = -18.

I hope this helps! Let me know if you have any further questions.