Question

State what method you are using to solve the system. Then solve the system. Show all steps of your work, clearly state your answer as a coordinate pair, and check it. 1. Y = −3x 4x + y = 2 2. Y = 7x − 5 2x + y = 13 3. X = −5y − 4 x − 4y = 23 4. −4x + 6y = −20 2x − 3y = 10 5. 3x − y = 1 −2x + y = 2 6. Y = − 3x y = 7 + 4x

Answer 1

To solve a system of equations, we use the method of substitution. We then solve for one variable and substitute it into the other equation. The solutions to the given systems of equations are (2, -6), (2, 9), (11, -3), (-5/2, -10/3), (3, 8), and (-1, 3).

Step-by-step explanation:

To solve a system of equations, we need to use the method of substitution. This involves solving one equation for one variable and then substituting that expression into the other equation.

Let's solve each system of equations:

Y = -3x and 4x + y = 2
Substitute -3x for Y in the second equation: 4x + (-3x) = 2. Simplify: x = 2. Substitute x = 2 into the first equation: Y = -6. So, the solution is (2, -6).

Y = 7x - 5 and 2x + y = 13
Substitute 7x - 5 for Y in the second equation: 2x + (7x - 5) = 13. Simplify: x = 2. Substitute x = 2 into the first equation: Y = 9. So, the solution is (2, 9).

X = -5y - 4 and x - 4y = 23
Substitute -5y - 4 for X in the second equation: (-5y - 4) - 4y = 23. Simplify: y = -3. Substitute y = -3 into the first equation: X = 11. So, the solution is (11, -3).

-4x + 6y = -20 and 2x - 3y = 10
Add the two equations to eliminate x: -4x + 6y + (2x - 3y) = -20 + 10. Simplify: 3y = -10. Solve for y: y = -10/3. Substitute y = -10/3 into the first equation: -4x + 6(-10/3) = -20. Simplify and solve for x: x = -5/2. So, the solution is (-5/2, -10/3).

3x - y = 1 and -2x + y = 2
Add the two equations to eliminate y: 3x - y + (-2x + y) = 1 + 2. Simplify: x = 3. Substitute x = 3 into the second equation: -2(3) + y = 2. Simplify and solve for y: y = 8. So, the solution is (3, 8).

Y = -3x and y = 7 + 4x
Set the two equations equal to each other and solve for x: -3x = 7 + 4x. Simplify and solve for x: x = -1. Substitute x = -1 into the second equation: y = 3. So, the solution is (-1, 3).

Answer 2

The method used is substitution method

x = 2, y = -6

Step-by-step explanation:

Given the simultaneous equation

Y = −3x ..... 1

4x + y = 2 ... 2

Substitute equation 1 into 2

4x + (-3x) = 2

4x - 3x = 2

x = 2

Get y:

y = -3x

y = -3(2)

y = -6

Hence the value of (x, y) is (2, -6)