Solve the simultaneous equations 𝑥 plus 𝑦 equals six and 𝑦 minus 19 equals zero.
In order to solve a pair of linear simultaneous equations, we need to find the value of 𝑥 and the value of 𝑦 that satisfy both of the equations. In this case, as there is no 𝑥 term in equation two, we will solve this first. If we add 19 to both sides of the equation 𝑦 minus 19 equals zero, we are left with 𝑦 equals 19.
Our next step is to substitute 𝑦 equals 19 into equation one. Replacing the 𝑦 with 19 gives us the equation 𝑥 plus 19 equals six. Subtracting 19 from both sides of this equation gives us an answer for 𝑥 equal to negative 13. Therefore, the solution to the simultaneous equations 𝑥 plus 𝑦 equals six and 𝑦 minus 19 equals zero is 𝑦 equals 19 and 𝑥 equals negative 13.
We can check this by substituting the values back into both of the equations. Equation one now reads negative 13 plus 19. This is equal to six. And equation two now reads 19 minus 19 which is equal to zero. Therefore, our solutions for 𝑥 and 𝑦 must be correct.