2x+3y=8
3x+2y=-1
To solve this system of equations algebraically, you can use the method of substitution or the method of elimination.
Let's use the method of elimination:
Step 1: Multiply the first equation by 2 and the second equation by 3 to make the coefficients of the x terms the same.
2(2x + 3y) = 2(8)
3(3x + 2y) = 3(-1)
This simplifies to:
4x + 6y = 16
9x + 6y = -3
Step 2: Subtract the first equation from the second equation to eliminate the y term.
(9x + 6y) - (4x + 6y) = -3 - 16
This simplifies to:
9x - 4x = -19
Step 3: Combine like terms and solve for x.
5x = -19
Divide both sides of the equation by 5 to isolate x:
x = -19/5
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the first equation:
2(-19/5) + 3y = 8
Simplify:
-38/5 + 3y = 8
Step 5: Solve for y.
To isolate y, subtract -38/5 from both sides of the equation:
3y = 8 + 38/5
To add the fractions, find a common denominator of 5:
3y = 40/5 + 38/5 = 78/5
Now divide both sides by 3 to solve for y:
y = (78/5) / 3 = 26/5
Therefore, the solution to the system of equations is:
x = -19/5
y = 26/5