Question

Solve the systems of equations and match them with the correct solution using subtraction.

a. 2x+3y=7 and 3x2y=4
b. 4x - 5y=2 and 2x+3y=10
c. 3x+2y=5 and 5x4y=8
d. x2y=3 and 2x+3y=7

Answer 1

To solve a system of equations using subtraction, you want to eliminate one variable by multiplying one or both of the equations by a constant so that the coefficients of either x or y will cancel out when the equations are subtracted. Follow the steps outlined above to solve each system of equations and find their solutions.

Step-by-step explanation:

To solve a system of equations using subtraction, you want to eliminate one variable by multiplying one or both of the equations by a constant so that the coefficients of either x or y will cancel out when the equations are subtracted.

Let's solve each system of equations using subtraction:

a. 2x + 3y = 7 and 3x + 2y = 4

Multiplying the first equation by 2 and the second equation by 3 gives us:

4x + 6y = 14 and 9x + 6y = 12

Subtracting the second equation from the first equation eliminates the y variable:

(4x + 6y) - (9x + 6y) = 14 - 12

-5x = 2

Dividing both sides by -5 gives us:

x = -2/5

Now we can substitute this value of x into one of the original equations to solve for y:

2(-2/5) + 3y = 7

-4/5 + 3y = 7

3y = 35/5 + 4/5

3y = 39/5

y = 13/5

So the solution to the system of equations is x = -2/5 and y = 13/5.