How do you solve the system by substitution?

1. \(6x + 2y = -26\)

2. \(x - 6y = 21\)

{ 6 x + 2 y = − 26 / ∗ 3 x − 6 y = 21 ​ { 18 x + 6 y = − 78 x − 6 y = 21 ​ + \- − − − − − − − − 19 x = − 57 / : 19 x = − 19 57 ​ x = − 3
x − 6 y = 21 − 3 − 6 y = 21 ∣3 − 3 + 3 − 6 y = 21 + 3 − 6 y = 24 / : ( − 6 ) y = − 6 24 ​ y = − 4 { x = − 3 y = − 4 ​

Answered by Lilith | 2024-06-10

The question involves solving a system of equations by substitution. We're given two equations: 6x+2y=-26 and x-6y=21. Let's use the second equation to express x in terms of y, and then substitute that expression into the first equation to solve for y.
From the second equation, x = 21 + 6y.
Substitute this expression for x into the first equation: 6(21 + 6y) + 2y = -26.
Simplify and solve for y: 126 + 36y + 2y = -26 → 38y = -152 → y = -4.
Substitute y = -4 into the expression for x: x = 21 + 6(-4) = 21 - 24 = -3.
Therefore, the solution to the system of equations is x = -3 and y = -4. To check, we can substitute these values back into the original equations and verify that they satisfy both equations, which they do.

Answered by TimothyJamesCurry | 2024-06-24

To solve the given system of equations using substitution, first solve one equation for a variable, substitute that expression into the other equation, and solve for the unknowns. This method yields the solution ( x , y ) = ( − 3 , − 4 ) .
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Answered by Lilith | 2024-10-11