Identify the solution:

2x + 3y = 3
y=-2x+9

(6, -3) aka x = 6 and y = -3

Step-by-step explanation:

since you are given y = -2x + 9, you should start by substituting the expression -2x + 9 for y in the equation 2x + 3y = 3.

here's your equation after plugging in the expression that's equal to y:

2x + 3(-2x + 9) = 3

distribute 3 to -2x

2x + 3(-2x + 9) = 3 ⇒ 3 · -2x = -6x

...and to 9.

2x + 3(-2x + 9) = 3 ⇒ 3 · 9 = 27

now you're left with 2x - 6x + 27 = 3.

combine like terms.

2x - 6x + 27 = 3 ⇒ -4x + 27 = 3

subtract 27 from both sides of the equation. since +27 and -27 cancel each other out, you're left with subtracting 27 from 3, which gives you -24.

now your equation is -4x = -24.

divide both sides of the equation by -4.

-24/-4 = 6

...therefore x = 6.

since you have your x value now, you can plug that into the equation for y in order to solve for y.

y = -2x + 9 ⇒ y = -2(6) + 9

multiply -2 and 6.

y = -2(6) + 9 ⇒ y = -12 + 9

add -12 and 9.

y = -12 + 9 ⇒ y = -3

...and now you've solved for y, which is -3.

therefore, your solution is (6, -3), aka x = 6 and y = -3.

hope this helps! have a nice day <3

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc