Q. Solve using elimination.−7x−6y=16−8x−9y=−1(_____,_____)
Write Equations: First, let's write down the system of equations we need to solve:−7x−6y=16−8x−9y=−1We want to eliminate one of the variables by making the coefficients of either x or y the same in both equations.
Eliminate Variable: To eliminate y, we can multiply the first equation by 9 and the second equation by 6 to get the coefficients of y to be the same.Multiplying the first equation by 9:(−7x−6y)×9=16×9−63x−54y=144Multiplying the second equation by 6:(−8x−9y)×6=−1×6−48x−54y=−6
New System: Now we have the new system of equations:−63x−54y=144−48x−54y=−6We can subtract the second equation from the first to eliminate y:(−63x−54y)−(−48x−54y)=144−(−6)−63x+48x=144+6−15x=150
Subtract Equations: Now we can solve for x by dividing both sides by −15:−15−15x=−15150x=−10
Solve for x: Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:−7x−6y=16Substitute x=−10:−7(−10)−6y=1670−6y=16
Substitute x: Now we can solve for y by subtracting 70 from both sides:70−70−6y=16−70−6y=−54
Solve for y: Finally, we divide both sides by −6 to find the value of y:−6−6y=−6−54y=9