Question

What is the solution
y=-x+2
y=-3x-2

Answer 1

Answer: (-2, 4)

Concept:

There are three general ways to solve systems of equations:

1. Elimination: using addition/subtraction to cancel out variables.
2. Substitution: when two variables appear in both equations and are isolated, they could substitute each other.
3. Graphing: graph the equations to find the intersection for the solution.

Here we are going to use substitution since the variable [y] is being isolated in both equations.

Solve:

Given equations

y = -x + 2

y = -3x - 2

Using the method of substitution to combine the equations

-x + 2 = -3x - 2

Add 3x on both sides

-x + 2 + 3x = -3x - 2 + 3x

2x + 2 = -2

Subtract 2 on both sides

2x + 2 - 2 = -2 - 2

2x = -4

Divide 2 on both sides

2x / 2 = -4 / 2

`\boxed{x=-2}`

Find the y value

y = -x + 2 →→→ Given expression

y = -(-2) + 2 →→→ Substitute values into the expression

y = 2 + 2 →→→ Simplify the value

`\boxed{y=4}` →→→ SImplify by addition

Hope this helps!! :)

Please let me know if you have any questions