Question

Solve the system of equations by graphing. Check the solution. y=-2x-3. y=2x+5. Graph each equation on the same coordinate plane. At what point do the graphs of the lines appear to intersect?​

Answer 1

`\displaystyle [-2, 1]`

Explanation:

Use the Elimination method sinse both coefficients in the system are OPPOCITES:

`\displaystyle \left \{{{y = -2x - 3} \atop {y = 2x + 5}} \right.`

2y = 2; 1 = y [Plug this y-coordinate back into the system to get the x-coordinate of −2 (−2 = x).]

I am joyous to assist you at any time.

Answer 2

`\left \{ {{x=-2} \atop {y=1}} \right.`

Explanation:

`\left \{ {{y=-2x-3} \atop {y=2x+5}} \right.`

Substitute into one of the equations

`-2x-3=2x+5`

Rearrange variables to the left side of the equation

`-2x-2x=5+3`

Combine like terms

`-4x=5+3`

Calculate the sum or difference

`-4x=8`

Divide both sides of the equation by the coefficient of variable

`x=-(8)/(4)`

Cross out the common factor

`x=-2`

Substitute into one of the equations

`y=-2*\left(-2\right)-3`

Calculate

`y=1`

The solution of the system is

`\left \{ {{x=-2} \atop {y=1}} \right.`

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