How do you solve by elimination this linear equation? 8x-3y=-6,
5x+6y=75
solve the linear system using elimination 10x-9y=46
To solve this system of linear equations by elimination, you need to eliminate one of the variables by manipulating the equations and combining them. Here's how to do it step by step:
Step 1: Multiply the two equations by appropriate constants so that the coefficients of one of the variables are equal but opposite in sign. In this case, we can multiply the first equation by 2 and the second equation by 3:
Equation 1: 16x - 6y = -12
Equation 2: 15x + 18y = 225
Step 2: Now, subtract the two equations to eliminate the variable y. Subtracting Equation 1 from Equation 2, we get:
(15x + 18y) - (16x - 6y) = 225 - (-12)
15x + 18y - 16x + 6y = 225 + 12
-x + 24y = 237
Step 3: Simplify the equation obtained in Step 2:
-x + 24y = 237
Step 4: Solve the resulting equation for one variable. In this case, let's solve for x by multiplying the entire equation by -1:
x - 24y = -237
Step 5: Now, add the original Equation 1 and this modified Equation from Step 4 to eliminate the variable x. Adding both equations, we get:
(8x - 3y) + (x - 24y) = -6 + (-237)
8x - 3y + x - 24y = -6 - 237
9x - 27y = -243
Step 6: Simplify the equation obtained in Step 5:
9x - 27y = -243
Step 7: Solve the resulting equation for the remaining variable. In this case, let's solve for y by dividing the entire equation by -27:
9x - 27y = -243
(-9x + 27y)/-27 = (-243)/-27
x - y = 9
So, the solution to the system of linear equations is x - y = 9.
To check the solution, substitute the values of x and y into the original equations and check if both equations are satisfied.
8x-3y=-6,
5x+6y=75
multiply the top one by 2
16x-6y=-12,
5x+6y=75
add the two together
21x=63
can you take it from here?