Systems of linear equations

Check whether the second equation coefficients are the first multiplied by one shared factor. If the right-hand side uses the same factor, the equations coincide and there are infinitely many solutions. If not, they contradict each other and there is no solution.

Adding x + y = s and 2x − y = t eliminates y: 3x = s + t. Find x, then use y = s − x.

Check whether the second equation coefficients are the first multiplied by one shared factor. If the right-hand side uses the same factor, the equations coincide and there are infinitely many solutions. If not, they contradict each other and there is no solution.

Adding ax + by = c1 and ax − by = c2 gives 2ax = c1 + c2. Subtracting the second equation from the first gives 2by = c1 − c2. Divide to find x and y.

Add x + y = s and x − y = d to obtain 2x = s + d. Thus x = (s + d)/2, then y = s − x. Check both equations.

In (x, y), the first number is x and the second is y. Substitute them and compare the two sides. A system solution must satisfy all its equations simultaneously.

In (x, y), the first number is x and the second is y. Substitute them and compare the two sides. A system solution must satisfy all its equations simultaneously.

Adding ax + by = c1 and ax − by = c2 gives 2ax = c1 + c2. Subtracting the second equation from the first gives 2by = c1 − c2. Divide to find x and y.

Let x be the A-ticket count and y the B-ticket count. Write x + y = total and a × x + b × y = revenue. Substitute y = total − x, solve for x, then find y. Give A first.

Let x be the A-ticket count and y the B-ticket count. Write x + y = total and a × x + b × y = revenue. Substitute y = total − x, solve for x, then find y. Give A first.