Finding the Solution to the System of Equations
To solve the system of equations given by y = x + 10 and 2x + y = 4, we can use the substitution method. This involves substituting one equation into the other to find the values of x and y. Let’s break this down step-by-step:
Step 1: Substitute y in the second equation
From the first equation, we know that y = x + 10. We can substitute this expression for y in the second equation:
2x + (x + 10) = 4
Step 2: Simplify the equation
Simplifying the left side gives:
2x + x + 10 = 4
3x + 10 = 4
Step 3: Solve for x
To isolate x, we need to subtract 10 from both sides:
3x = 4 – 10
3x = -6
Now, divide both sides by 3:
x = -2
Step 4: Substitute x back to find y
Now that we have the value of x, we can substitute x = -2 back into the first equation to find y:
y = -2 + 10
y = 8
Final Solution
So, the solution to the system of equations is:
(x, y) = (-2, 8)
This means that the lines represented by the equations intersect at the point (-2, 8). To ensure our solution is correct, we can substitute these values back into both original equations and confirm that they hold true.