solve the system. 4x-6y=-26; -2×+3y=13

Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

Method 1: Substitution
Let's solve one equation for one variable and substitute it into the other equation.

From the equation -2x + 3y = 13, we can solve it for x:
-2x = -13 - 3y
x = (13+3y)/2

Now substitute this expression for x into the first equation:
4((13+3y)/2) - 6y = -26

Multiply both sides by 2 to eliminate the fraction:
4(13+3y) - 12y = -52
52 + 12y - 12y = -52
52 = -52

This equation implies that there is no solution to the system of equations. The two equations represent parallel lines that will never intersect.

Method 2: Elimination
Let's multiply the second equation by 2 and add it to the first equation to eliminate x:

4x - 6y = -26 (equation 1)
-4x + 6y = 26 (equation 2 multiplied by -2)

Adding both equations gives:
0 = 0

In this case, the variables are eliminated and we are left with a true statement 0 = 0. This means that the system is dependent and there are infinitely many solutions. The two equations represent the same line and, therefore, intersect at all points along that line in the coordinate plane.