Question

2x+3y=15
use elimination to solve the system of equations

Answer 1

To solve the system of equations using elimination, we need to add or subtract the equations to eliminate one of the variables.

Given equations:
1) 2x + 3y = 15
2) x - 2y = -4

First, we can multiply the second equation by 2 to balance the coefficients of x:

2(x - 2y) = 2(-4)
2x - 4y = -8

Now, we can add this equation to the first equation to eliminate x:

2x + 3y + 2x - 4y = 15 - 8
4x - y = 7

Now, we have a new equation with one variable, y. Let's solve for y:

4x - y = 7
y = 4x - 7

Substitute this expression for y back into one of the original equations (I will use the first equation):

2x + 3(4x - 7) = 15
2x + 12x - 21 = 15
14x - 21 = 15
14x = 36
x = 36/14
x = 18/7

Now that we have found the value of x, we can substitute it back into the equation y = 4x - 7 to find y:

y = 4(18/7) - 7
y = 72/7 - 49/7
y = 23/7

Therefore, the solution to the system of equations is:
x = 18/7
y = 23/7