Solve the systems of equations

Question

Solve the system of equations using elimination: 4x+2y=-60 and -x-y=20

Answer 1

Equals added to equals are equal. So we can add the equations:

4x+2y= -60

-x-y=20

Adding:

3x + y = -40

Well that did not help because a variable did not get eliminated. Try multiplying the 2nd equation by 2 (multiplication for equality guarantees that the new equation has the same solution set).

4x + 2y = -60

-2x -2y = 40

Now when the equations are added the y variable is eliminated:

2x + 0 = -20

x = -10

When x = -10 use either equation to solve for y:

-(-10) - y = 20

10 - y = 20

-y = 10

y = -10

The solution set:

x = -10

y =-10

Check:

4(-10) + 2(-10) = -40-20=-60 check.

-(-10)-(-10) = 10 + 10 = 20 check.

The point (-10,-10) is the point of intersection for the graphs of these two equations.

desmos.com/calculator/r7r7blustl

This is not the only way to perform the elimination. For example, the first equation could have been divided by 2 (or multiplied by 1/2).

Or the 2nd equation could have been multiplied by 4 and the x variable eliminated.

For some systems both equations must be modified in order to eliminate a variable.

For example:

3x + 2y = 7

2x - 5y = -3

Multiply 1st equation by 2 and the 2nd equation by -3 to get 6x and -6x as the coefficients of x. Then adding eliminates x.

Give it a try and check here:

desmos.com/calculator/r3a7xiuvyr