5x+6y=37

2x-3y=-4

what are we doing?

solving?

keep the first as is: 5x+6y=37
double the second: 4x - 6y = -8
add them
9x = 29
x = 29/9

in the 1st:
5(29/9) + 6y = 37
times 9
145 + 54y = 333
54y = 188
y = 188/54 = 94/27

x = 29/9 , y = 94/27

2x-3y =-4 5x+6y=7

To find the solution to these two equations, you can use the method of substitution or elimination.

Let's use the method of substitution.

Step 1: Solve one of the equations for one variable.
We can solve the second equation for x:
2x - 3y = -4

Rearrange the equation to isolate x:
2x = 3y - 4
Divide both sides by 2:
x = (3y - 4)/2

Step 2: Substitute the expression for x in the other equation.
Now substitute (3y - 4)/2 for x in the first equation:
5x + 6y = 37
5((3y - 4)/2) + 6y = 37
(15y - 20)/2 + 6y = 37
15y - 20 + 12y = 74
27y - 20 = 74

Step 3: Solve for y.
Add 20 to both sides:
27y = 94
Divide both sides by 27:
y = 94/27

Step 4: Substitute the value of y back into either of the original equations to solve for x.
Let's use the second equation:
2x - 3(94/27) = -4
2x - 282/27 = -4
Multiply both sides by 27 to get rid of the fraction:
54x - 282 = -108
54x = -108 + 282
54x = 174
Divide both sides by 54:
x = 174/54

Simplifying the fraction gives:
x = 3.22

Therefore, the solution to the system of equations is x = 3.22 and y = 3.48 (rounded to two decimal places).